Deck 8: Systems of Equations

ملء الشاشة (f)
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سؤال
Solve graphically.
2x+y=22x+2y=4\begin{array} { l } 2 x + y = - 2 \\2 x + 2 y = 4\end{array}
 <strong>Solve graphically.  \begin{array} { l } 2 x + y = - 2 \\ 2 x + 2 y = 4 \end{array}    </strong> A)  ( 4,6 )  В)  ( - 4,6 )  C)  ( 2 , - 6 )  D)  ( - 4 , - 5 )  <div style=padding-top: 35px>

A) (4,6)( 4,6 )
В) (4,6)( - 4,6 )
C) (2,6)( 2 , - 6 )
D) (4,5)( - 4 , - 5 )
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لقلب البطاقة.
سؤال
Classify the system as consistent or inconsistent, and dependent or independent.
2x4y=2y=12x12\begin{array} { l } 2 x - 4 y = 2 \\y = \frac { 1 } { 2 } x - \frac { 1 } { 2 }\end{array}

A) Consistent and dependent
B) Consistent and independent
C) Inconsistent and dependent
D) Inconsistent and independent
سؤال
Classify the system as consistent or inconsistent, and dependent or independent.
x+y=11xy=5\begin{array} { l } x + y = - 11 \\x - y = - 5\end{array}

A) Inconsistent and independent
B) Inconsistent and dependent
C) Consistent and dependent
D) Consistent and independent
سؤال
Solve graphically.
3x+4y=314x2y=34\begin{array} { l } 3 x + 4 y = 31 \\4 x - 2 y = 34\end{array}
 <strong>Solve graphically.  \begin{array} { l } 3 x + 4 y = 31 \\ 4 x - 2 y = 34 \end{array}    </strong> A) No solution B)  ( 1,9 )  C)  ( 3,22 )  D)  ( 9,1 )  <div style=padding-top: 35px>

A) No solution
B) (1,9)( 1,9 )
C) (3,22)( 3,22 )
D) (9,1)( 9,1 )
سؤال
Solve graphically.
32x13y=552x+23y=12\begin{array} { l } \frac { 3 } { 2 } x - \frac { 1 } { 3 } y = 5 \\\frac { 5 } { 2 } x + \frac { 2 } { 3 } y = 12\end{array}
 <strong>Solve graphically.  \begin{array} { l } \frac { 3 } { 2 } x - \frac { 1 } { 3 } y = 5 \\ \frac { 5 } { 2 } x + \frac { 2 } { 3 } y = 12 \end{array}    </strong> A)  ( 4 , - 3 )  В)  ( 3,4 )  C)  ( 4,3 )  D)  ( 3,1 )  <div style=padding-top: 35px>

A) (4,3)( 4 , - 3 )
В) (3,4)( 3,4 )
C) (4,3)( 4,3 )
D) (3,1)( 3,1 )
سؤال
Classify the system as consistent or inconsistent, and dependent or independent.
3x=y+36x2y=3\begin{array} { l } 3 x = y + 3 \\6 x - 2 y = 3\end{array}

A) Inconsistent and dependent
B) Consistent and independent
C) Inconsistent and independent
D) Consistent and dependent
سؤال
Classify the system as consistent or inconsistent, and dependent or independent.
x8=yy+2=x\begin{array} { l } x - 8 = y \\y + 2 = x\end{array}

A) Inconsistent and independent
B) Consistent and independent
C) Consistent and dependent
D) Inconsistent and dependent
سؤال
Classify the system as consistent or inconsistent, and dependent or independent.
x+5y=195x6y=2\begin{array} { c } x + 5 y = 19 \\5 x - 6 y = 2\end{array}

A) Inconsistent and independent
B) Consistent and independent
C) Consistent and dependent
D) Inconsistent and dependent
سؤال
Solve graphically.
2x+y=64x+2y=12\begin{array}{l}2 x+y=6 \\4 x+2 y=12\end{array}
 <strong>Solve graphically.  \begin{array}{l} 2 x+y=6 \\ 4 x+2 y=12 \end{array}   </strong> A) No solution B) Infinite number of solutions C)  ( 0,6 )  D)  ( 5 , - 4 )  <div style=padding-top: 35px>

A) No solution
B) Infinite number of solutions
C) (0,6)( 0,6 )
D) (5,4)( 5 , - 4 )
سؤال
Solve using the substitution method.
x+y=16y=3x+4\begin{array} { l } x + y = 16 \\y = 3 x + 4\end{array}

A) (4,12)( 4,12 )
B) (2,16)( 2,16 )
C) (3,13)( 3,13 )
D) (13,3)( 13,3 )
سؤال
Solve graphically.
x=yy+x=6\begin{array}{l}x=-y \\y+x=6\end{array}
 <strong>Solve graphically.  \begin{array}{l} x=-y \\ y+x=6 \end{array}   </strong> A)  ( 1,5 )  B) No solution C)  ( 1,1 )  D) Infinite number of solutions <div style=padding-top: 35px>

A) (1,5)( 1,5 )
B) No solution
C) (1,1)( 1,1 )
D) Infinite number of solutions
سؤال
Classify the system as consistent or inconsistent, and dependent or independent.
10x2y=105xy=5\begin{array} { c } - 10 x - 2 y = 10 \\5 x - y = - 5\end{array}

A) Consistent and independent
B) Inconsistent and independent
C) Inconsistent and dependent
D) Consistent and dependent
سؤال
Solve graphically.
3x+2y=56x4y=5\begin{array}{c}3 x+2 y=5 \\-6 x-4 y=5\end{array}
 <strong>Solve graphically.  \begin{array}{c} 3 x+2 y=5 \\ -6 x-4 y=5 \end{array}   </strong> A)  ( 1.5 , - 1 )  B) No solution C)  ( 1,1 )  D)  ( - 1.5 , - 1 )  <div style=padding-top: 35px>

A) (1.5,1)( 1.5 , - 1 )
B) No solution
C) (1,1)( 1,1 )
D) (1.5,1)( - 1.5 , - 1 )
سؤال
Classify the system as consistent or inconsistent, and dependent or independent.
x+6y=172x+12y=34\begin{array} { c } x + 6 y = 17 \\2 x + 12 y = 34\end{array}

A) Inconsistent and dependent
B) Consistent and dependent
C) Inconsistent and independent
D) Consistent and independent
سؤال
Solve using the substitution method.
y=2x44x+y=28\begin{array} { l } y = 2 x - 4 \\4 x + y = - 28\end{array}

A) (5,14)( - 5 , - 14 )
В) (12,4)( - 12 , - 4 )
C) (12,20)( - 12,20 )
D) (4,12)( - 4 , - 12 )
سؤال
Solve graphically.
3x2y=46x+4y=7\begin{array}{c}3 x-2 y=4 \\-6 x+4 y=7\end{array}
 <strong>Solve graphically.  \begin{array}{c} 3 x-2 y=4 \\ -6 x+4 y=7 \end{array}   </strong> A) Infinite number of solutions B)  ( 2,1 )  C) No solution D)  ( 1,2 )  <div style=padding-top: 35px>

A) Infinite number of solutions
B) (2,1)( 2,1 )
C) No solution
D) (1,2)( 1,2 )
سؤال
Classify the system as consistent or inconsistent, and dependent or independent.
4x+4y=18x+8y=2\begin{array} { l } 4 x + 4 y = 1 \\8 x + 8 y = 2\end{array}

A) Inconsistent and dependent
B) Consistent and dependent
C) Inconsistent and independent
D) Consistent and independent
سؤال
Classify the system as consistent or inconsistent, and dependent or independent.
x+y=82x2y=8\begin{array} { c } x + y = 8 \\2 x - 2 y = 8\end{array}

A) Inconsistent and dependent
B) Consistent and dependent
C) Consistent and independent
D) Inconsistent and independent
سؤال
Solve graphically.
x=2y=1\begin{array} { l } x = - 2 \\y = 1\end{array}
 <strong>Solve graphically.  \begin{array} { l } x = - 2 \\ y = 1 \end{array}    </strong> A) Infinitely many solutions B) No solution C)  ( - 2,1 )  D)  ( 1 , - 2 )  <div style=padding-top: 35px>

A) Infinitely many solutions
B) No solution
C) (2,1)( - 2,1 )
D) (1,2)( 1 , - 2 )
سؤال
Classify the system as consistent or inconsistent, and dependent or independent.
x3y=63y+1=x\begin{array} { r } x - 3 y = 6 \\3 y + 1 = x\end{array}

A) Consistent and independent
B) Inconsistent and independent
C) Consistent and dependent
D) Inconsistent and dependent
سؤال
Solve using the elimination method.
x+y=11x + y = 11 xy=7x - y = 7

A) No solution
B) (9,2)( 9,2 )
C) (8,3)( 8,3 )
D) (9,3)( - 9,3 )
سؤال
Solve by the substitution method.
x+y=75x+5y=35\begin{array} { c } x + y = 7 \\5 x + 5 y = 35\end{array}

A) (0,0)( 0,0 )
B) Infinite number of solutions
C) (7,5)( 7,5 )
D) (8,1)( 8 , - 1 )
سؤال
Solve by the substitution method.
x5y=276x6y=90\begin{array} { l } x - 5 y = - 27 \\- 6 x - 6 y = - 90\end{array}

A) No solution
В) (8,8)( - 8,8 )
C) (7,8)( 7,8 )
D) (8,7)( 8,7 )
سؤال
Solve the problem.
The sum of two numbers is 34 and their difference is 12. Find the numbers.

A)23 and 11
B)25 and 37
C)9 and 25
D)11 and 23
سؤال
Solve by the substitution method.
x+y=1x+y=4\begin{array} { l } x + y = - 1 \\x + y = 4\end{array}

A) (0,3)( 0,3 )
B) No solution
C) (0,0)( 0,0 )
D) (1,4)( - 1,4 )
سؤال
Solve by the substitution method.
x+6y=17x+7y=7\begin{array} { l } x + 6 y = - 1 \\7 x + 7 y = - 7\end{array}

A) (1,0)( - 1,0 )
B) (0,1)( 0 , - 1 )
C) (1,1)( 1 , - 1 )
D) No solution
سؤال
Solve using the elimination method.
4xy=195x+y=35\begin{array} { l } 4 x - y = 19 \\5 x + y = 35\end{array}

A) (5,6)( 5,6 )
B) (6,5)( 6,5 )
C) (6,6)( 6,6 )
D) No solution
سؤال
Solve the problem.
The perimeter of a rectangle is 78 m78 \mathrm {~m} . If the width were doubled and the length were increased by 12 m12 \mathrm {~m} , the perimeter would be 132 m132 \mathrm {~m} . What are the length and width of the rectangle?

A) width 19 m19 \mathrm {~m} , length 19 m19 \mathrm {~m}
B) width 14 m14 \mathrm {~m} , length 19 m19 \mathrm {~m}
C) width 15 m15 \mathrm {~m} , length 24 m24 \mathrm {~m}
D) width 24 m24 \mathrm {~m} , length 15 m15 \mathrm {~m}
سؤال
Solve using the substitution method.
x=1+2yx+2y=8\begin{array} { l } x = 1 + - 2 y \\x + 2 y = 8\end{array}

A) Infinitely many solutions
B) (7,15)( - 7,15 )
C) (7,15)( - 7 , - 15 )
D) No solution
سؤال
Solve by the substitution method.
8x+8y=325x4y=20\begin{array} { l } 8 x + 8 y = - 32 \\5 x - 4 y = - 20\end{array}

A) (5,1)( - 5,1 )
B) No solution
C) (4,0)( - 4,0 )
D) (4,1)( - 4,1 )
سؤال
Solve the problem.
Two angles have a sum of 8181 ^ { \circ } . Their difference is 1515 ^ { \circ } . Find the angles.

A) 6767 ^ { \circ } and 1414 ^ { \circ }
B) 3535 ^ { \circ } and 5050 ^ { \circ }
C) 4848 ^ { \circ } and 3333 ^ { \circ }
D) 4646 ^ { \circ } and 3535 ^ { \circ }
سؤال
Solve the problem.
The perimeter of a triangle is 65 cm65 \mathrm {~cm} . The triangle is isosceles now, but if its base were lengthened by 6 cm6 \mathrm {~cm} and each leg were shortened by 7 cm7 \mathrm {~cm} , it would be equilateral. Find the base of the original triangle.

A) 19 cm19 \mathrm {~cm}
B) 26 cm26 \mathrm {~cm}
C) 13 cm13 \mathrm {~cm}
D) 12 cm12 \mathrm {~cm}
سؤال
Solve the problem.
The perimeter of a rectangle is 56 cm56 \mathrm {~cm} . One side is 12 cm12 \mathrm {~cm} longer than the other side. Find the lengths of the sides.

A) 8 cm,20 cm8 \mathrm {~cm} , 20 \mathrm {~cm}
B) 11 cm,23 cm11 \mathrm {~cm} , 23 \mathrm {~cm}
C) 8 cm,12 cm8 \mathrm {~cm} , 12 \mathrm {~cm}
D) 16 cm,28 cm16 \mathrm {~cm} , 28 \mathrm {~cm}
سؤال
Solve by the substitution method.
7x+9y=543x4y=24\begin{array} { c } 7 x + 9 y = - 54 \\- 3 x - 4 y = 24\end{array}

A) (1,5)( - 1 , - 5 )
B) (0,5)( 0 , - 5 )
C) No solution
D) (0,6)( 0 , - 6 )
سؤال
Solve by the substitution method.
6x+9y=1144x4y=4\begin{array} { l } 6 x + 9 y = 114 \\4 x - 4 y = - 4\end{array}

A) No solution
B) (7,9)( 7,9 )
C) (6,9)( 6,9 )
D) (7,8)( 7,8 )
سؤال
Solve by the substitution method.
x+3y=187x+4y=24\begin{array} { r } x + 3 y = 18 \\7 x + 4 y = 24\end{array}

A) (0,6)( 0,6 )
B) No solution
C) (6,0)( - 6,0 )
D) (1,5)( 1,5 )
سؤال
Solve the problem.
Find two numbers whose sum is 40 and whose difference is 12.

A)29 and 11
B)26 and 14
C)24 and 16
D)16 and 28
سؤال
Solve using the elimination method.
x3y=25x+3y=46\begin{array} { l } - x - 3 y = - 2 \\- 5 x + 3 y = - 46\end{array}

A) (8,2)( 8 , - 2 )
B) No solution
C) (9,3)( 9 , - 3 )
D) (2,8)( 2,8 )
سؤال
Solve the problem.
The sum of two angles is 225225 ^ { \circ } . One angle is 3030 ^ { \circ } less than twice the other. Find the angles.

A) 136136 ^ { \circ } and 8989 ^ { \circ }
B) 8585 ^ { \circ } and 140140 ^ { \circ }
C) 8383 ^ { \circ } and 142142 ^ { \circ }
D) 8383 ^ { \circ } and 136136 ^ { \circ }
سؤال
Solve by the substitution method.
8x+17=9y6x2y=4\begin{array} { l } 8 x + 17 = 9 y \\- 6 x - 2 y = 4\end{array}

A) (1,2)( - 1,2 )
B) No solution
C) (2,2)( - 2,2 )
D) (1,1)( - 1,1 )
سؤال
Solve the problem using the elimination method.
Two angles are supplementary, and one is 4040 ^ { \circ } more than three times the other. Find the smaller angle.

A) 145145 ^ { \circ }
B) 105105 ^ { \circ }
C) 7575 ^ { \circ }
D) 3535 ^ { \circ }
سؤال
Solve the system of equations by the elimination method.
32x13y=1834x+29y=9\begin{array} { l } \frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 18 \\\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 9\end{array}

A) (12,0)( - 12,0 )
B) (0,12)( 0 , - 12 )
C) (0,12)( 0,12 )
D) (12,0)( 12,0 )
سؤال
Solve the system of equations by the elimination method.
x+5y=24x+6y=8\begin{array} { c } x + 5 y = 2 \\- 4 x + 6 y = - 8\end{array}

A) (2,0)( 2,0 )
B) no solution
C) (3,2)( 3,2 )
D) (2,1)( - 2 , - 1 )
سؤال
Solve the problem using the elimination method.
There were 490 people at a play. The admission price was $3\$ 3 for adults and $1\$ 1 for children. The admission receipts were $1070\$ 1070 . How many adults and how many children attended?

A) 290 adults and 200 children
B) 267 adults and 223 children
C) 100 adults and 390 children
D) 200 adults and 290 children
سؤال
Solve the system of equations by the elimination method.
5x6y=515x18y=15\begin{array} { l } 5 x - 6 y = - 5 \\15 x - 18 y = 15\end{array}

A) no solution
B) (25,30)( 25 , - 30 )
C) infinitely many solutions
D) (25,30)( - 25,30 )
سؤال
Solve the problem using the elimination method.
Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $81\$ 81 for 3 days and 300 miles, while Mary was charged $145\$ 145 for 5 days and 600 miles. What does Best Rental charge per day and per mile?

A) $18\$ 18 per day and 1111 \nsubseteq per mile
B) $10\$ 10 per day and 17517 \nsubseteq 5 per mile
C) $16\$ 16 per day and 1111 \nsubseteq \subset per mile
D) $17\$ 17 per day and 1010 \simeq per mile
سؤال
Solve the system of equations by the elimination method.
7x6y=363x+4y=24\begin{array} { l } - 7 x - 6 y = - 36 \\- 3 x + 4 y = 24\end{array}

A) no solution
B) (0,7)( 0,7 )
C) (0,6)( 0,6 )
D) (1,7)( - 1,7 )
سؤال
Solve the system of equations by the elimination method.
0.3x+0.5y=3.1x0.1y=1.5\begin{array} { r } 0.3 x + 0.5 y = 3.1 \\x - 0.1 y = 1.5\end{array}

A) (0.2,0.5)( 0.2,0.5 )
B) (5,2)( 5,2 )
C) no solution
D) (2,5)( 2,5 )
سؤال
Solve the system of equations by the elimination method.
x+3y=156x+4y=20\begin{array} { c } x + 3 y = 15 \\- 6 x + 4 y = 20\end{array}

A) no solution
B) (1,4)( 1,4 )
C) (5,0)( - 5,0 )
D) (0,5)( 0,5 )
سؤال
Solve using the elimination method.
x+6y=262x+6y=22\begin{array} { c } x + 6 y = 26 \\2 x + 6 y = 22\end{array}

A) (4,4)( 4,4 )
B) No solution
C) (4,5)( - 4,5 )
D) (3,4)( - 3 , - 4 )
سؤال
Solve the system of equations by the elimination method.
3x5y=218x30y=12\begin{array} { l } 3 x - 5 y = 2 \\18 x - 30 y = 12\end{array}

A) (6,10)( 6 , - 10 )
B) infinitely many solutions
C) (10,6)( - 10,6 )
D) no solution
سؤال
Solve the system of equations by the elimination method.
9x+9y=454x6y=20\begin{array} { l } 9 x + 9 y = - 45 \\- 4 x - 6 y = 20\end{array}

A) (5,1)( - 5,1 )
B) no solution
C) (5,0)( - 5,0 )
D) (6,1)( - 6,1 )
سؤال
Solve the problem using the elimination method.
A salesman sold $200\$ 200 more than the rest of the sales staff. If the sales total for the day was $2050\$ 2050 , how much did the rest of the sales staff sell?

A) $1125\$ 1125
B) $925\$ 925
C) $1850\$ 1850
D) $1025\$ 1025
سؤال
Solve the problem using the elimination method.
In a right triangle, one acute angle is 5454 ^ { \circ } more than twice the other. Find each acute angle.

A) 1212 ^ { \circ } and 7878 ^ { \circ }
B) 3737 ^ { \circ } and 5353 ^ { \circ }
C) 2121 ^ { \circ } and 6969 ^ { \circ }
D) 2828 ^ { \circ } and 6262 ^ { \circ }
سؤال
Solve the system of equations by the elimination method.
32x13y=21\frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 21
34x+29y=7\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 7

A) (12,9)( - 12,9 )
В) (12,9)( 12,9 )
C) (12,9)( - 12 , - 9 )
D) (9,12)( 9 , - 12 )
سؤال
Solve the problem using the elimination method.
There were 38,000 people at a ball game in Los Angeles. The day's receipts were $229,000\$ 229,000 . How many people paid $11\$ 11 for reserved seats and how many paid $4\$ 4 for general admission?

A) 19,250 paid $11\$ 11 and 18,750 paid $4\$ 4
B) 27,000 paid $11\$ 11 and 11,000 paid $4\$ 4
C) 18,750 paid $11\$ 11 and 19,250 paid $4\$ 4
D) 11,000 paid $11\$ 11 and 27,000 paid $4\$ 4
سؤال
Solve the problem using the elimination method.
Two angles are supplementary, and one is 55 ^ { \circ } more than six times the other. Find the larger angle.

A) 2525 ^ { \circ }
B) 155155 ^ { \circ }
C) 7070 ^ { \circ }
D) 110110 ^ { \circ }
سؤال
Solve the system of equations by the elimination method.
0.8x+0.4y=4.8- 0.8 x + 0.4 y = 4.8 0.1x0.1y=0.70.1 x - 0.1 y = - 0.7

A) (50,20)( - 50,20 )
В) (0.5,0.2)( - 0.5,0.2 )
C) (5,2)( - 5,2 )
D) (2,5)( 2 , - 5 )
سؤال
Solve the system of equations by the elimination method.
2.5x+0.3y=10.60.5x+0.9y=3.8\begin{array} { l } 2.5 x + 0.3 y = 10.6 \\0.5 x + 0.9 y = 3.8\end{array}

A) (6.5,2.3)( 6.5,2.3 )
B) (4,2)( 4,2 )
C) (4.5,2)( 4.5,2 )
D) (1.5,2.3)( 1.5,2.3 )
سؤال
Solve the system of equations by the elimination method.
x3y=54x4y=12\begin{array} { c } x - 3 y = - 5 \\4 x - 4 y = 12\end{array}
4x4y=124 \mathrm { x } - 4 \mathrm { y } = 12

A) (7,4)( 7,4 )
В) (6,5)( 6,5 )
C) no solution
D) (7,5)( - 7,5 )
سؤال
Solve the problem using the elimination method.
The sum of two numbers is 100 . The second number is three times as large as the first number. What are the numbers?

A) 22 and 78
B) 23 and 69
C) 23 and 77
D) 25 and 75
سؤال
Solve the problem.
A merchant has coffee worth $20\$ 20 a pound that she wishes to mix with 90 pounds of coffee worth $90\$ 90 a pound to get a mixture that can be sold for $80\$ 80 a pound. How many pounds of the $20\$ 20 coffee should be used?

A) 7.5lb7.5 \mathrm { lb }
B) 52.5lb52.5 \mathrm { lb }
C) 105lb105 \mathrm { lb }
D) 15lb15 \mathrm { lb }
سؤال
Solve the problem.
There were 670 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $1020. How many adults and how many children attended?

A)320 adults and 350 children
B)255 adults and 415 children
C)350 adults and 320 children
D)160 adults and 510 children
سؤال
Solve the problem.
Anne and Nancy use a metal alloy that is 16%16 \% copper to make jewelry. How many ounces of an alloy that is 10%10 \% copper must be mixed with an alloy that is 20%20 \% copper to form 55 ounces of the desired alloy?

A) 22 ounces
B) 33 ounces
C) 38 ounces
D) 24 ounces
سؤال
Solve the problem.
Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 28 coins with a total face value of $5.00\$ 5.00 , how many of the coins are nickels?

A) 23 nickels
B) 10 nickels
C) 12 nickels
D) 18 nickels
سؤال
Solve the problem.
Walt made an extra $10,000\$ 10,000 last year from a part-time job. He invested part of the money at 10%10 \% and the rest at 9%9 \% . He made a total of $960\$ 960 in interest. How much was invested at 9%9 \% ?

A) $8000\$ 8000
B) $5000\$ 5000
C) $6000\$ 6000
D) $4000\$ 4000
سؤال
Solve the problem.
Andy has 33 coins made up of quarters and half dollars, and their total value is $13.25\$ 13.25 . How many quarters does he have?

A) 18 quarters
B) 22 quarters
C) 20 quarters
D) 13 quarters
سؤال
Solve the problem.
Ellen wishes to mix candy worth $1.79\$ 1.79 per pound with candy worth $3.75\$ 3.75 per pound to form 22 pounds of a mixture worth $2.95\$ 2.95 per pound. How many pounds of the more expensive candy should she use?

A) 13 pounds
B) 11 pounds
C) 9 pounds
D) 18 pounds
سؤال
Solve the problem.
Mardi received an inheritance of $60,000\$ 60,000 . She invested part at 8%8 \% and deposited the remainder in tax-free bonds at 11%11 \% . Her total annual income from the investments was $5700\$ 5700 . Find the amount invested at 8%8 \% .

A) $54,300\$ 54,300
B) $29,000\$ 29,000
C) $30,000\$ 30,000
D) $15,000\$ 15,000
سؤال
Solve the problem.
A sum of money amounting to $3.45\$ 3.45 consists of dimes and quarters. If there are 18 coins in all, how many are quarters?

A) 16 quarters
B) 7 quarters
C) 11 quarters
D) 9 quarters
سؤال
Solve the problem.
How many liters of a 20%20 \% alcohol solution must be mixed with 90 liters of a 80%80 \% solution to get a 40%40 \% solution?

A) 27 L27 \mathrm {~L}
B) 18 L18 \mathrm {~L}
C) 180 L180 \mathrm {~L}
D) 270 L270 \mathrm {~L}
سؤال
Solve the problem using the elimination method.
The sum of two numbers is 41 . The larger number minus the smaller number is 9 . What are the numbers?

A) 18 and 27
B) 25 and 16
C) 33 and 8
D) 23 and 18
سؤال
Solve the problem.
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 28 pounds of feed worth $0.62\$ 0.62 per pound by mixing one kind worth $0.15\$ 0.15 per pound with another worth $0.97\$ 0.97 per pound. How many pounds of the cheaper kind should they use in the mix?

A) 21 pounds
B) 14 pounds
C) 12 pounds
D) 16 pounds
سؤال
Solve the problem.
A woman made a deposit of $267. If her deposit consisted of 91 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

A)44 one-dollars
B)42 one-dollars
C)37 one-dollars
D)47 one-dollars
سؤال
Solve the problem.
In a chemistry class, 6 liters of a 4%4 \% silver iodide solution must be mixed with a 10%10 \% solution to get a 6%6 \% solution. How many liters of the 10%10 \% solution are needed?

A) 4.0 L4.0 \mathrm {~L}
B) 3.0 L3.0 \mathrm {~L}
C) 2.0 L2.0 \mathrm {~L}
D) 6.0 L6.0 \mathrm {~L}
سؤال
Solve the problem using the elimination method.
In a basketball game, Will scored 40 points, consisting only of three-point shots and two-point shots. He made a total of 17 shots. How many shots of each type did he make?

A) two-point shots: 11 ; three-point shots: 6
B) two-point shots: 6; three-point shots: 11
C) two-point shots: 10 ; three-point shots: 7
D) two-point shots: 12; three-point shots: 5
سؤال
Solve the problem using the elimination method.
A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $5.00\$ 5.00 . Another customer buys 4 hot dogs and 3 bags of potato chips for $9.00\$ 9.00 . Find the cost of each item.

A) $1.75\$ 1.75 for a hot dog; $1.25\$ 1.25 for a bag of potato chips
B) $1.50\$ 1.50 for a hot dog; $1.25\$ 1.25 for a bag of potato chips
C) $1.00\$ 1.00 for a hot dog; $1.50\$ 1.50 for a bag of potato chips
D) $1.50\$ 1.50 for a hot dog; $1.00\$ 1.00 for a bag of potato chips
سؤال
Solve the problem.
A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 9%9 \% cement should he mix with 10 bags of 10.8%10.8 \% cement to produce a mix containing 10%10 \% cement?

A) 23 bags
B) 10 bags
C) 8 bags
D) 18 bags
سؤال
Solve the problem.
Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $3.00 each and Kathy selling adult tickets for $5.50 each. If their total income for 25 tickets was $120.00, how many did Ron sell?

A)23 tickets
B)18 tickets
C)7 tickets
D)9 tickets
سؤال
Solve the problem using the elimination method.
The sum of two numbers is 4 . Three times the larger number plus two times the smaller number is 37 . Find the numbers.

A) 25 and 21- 21
B) 33 and 29- 29
C) 29 and 25- 25
D) 25 and 29- 29
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Deck 8: Systems of Equations
1
Solve graphically.
2x+y=22x+2y=4\begin{array} { l } 2 x + y = - 2 \\2 x + 2 y = 4\end{array}
 <strong>Solve graphically.  \begin{array} { l } 2 x + y = - 2 \\ 2 x + 2 y = 4 \end{array}    </strong> A)  ( 4,6 )  В)  ( - 4,6 )  C)  ( 2 , - 6 )  D)  ( - 4 , - 5 )

A) (4,6)( 4,6 )
В) (4,6)( - 4,6 )
C) (2,6)( 2 , - 6 )
D) (4,5)( - 4 , - 5 )
B
2
Classify the system as consistent or inconsistent, and dependent or independent.
2x4y=2y=12x12\begin{array} { l } 2 x - 4 y = 2 \\y = \frac { 1 } { 2 } x - \frac { 1 } { 2 }\end{array}

A) Consistent and dependent
B) Consistent and independent
C) Inconsistent and dependent
D) Inconsistent and independent
A
3
Classify the system as consistent or inconsistent, and dependent or independent.
x+y=11xy=5\begin{array} { l } x + y = - 11 \\x - y = - 5\end{array}

A) Inconsistent and independent
B) Inconsistent and dependent
C) Consistent and dependent
D) Consistent and independent
D
4
Solve graphically.
3x+4y=314x2y=34\begin{array} { l } 3 x + 4 y = 31 \\4 x - 2 y = 34\end{array}
 <strong>Solve graphically.  \begin{array} { l } 3 x + 4 y = 31 \\ 4 x - 2 y = 34 \end{array}    </strong> A) No solution B)  ( 1,9 )  C)  ( 3,22 )  D)  ( 9,1 )

A) No solution
B) (1,9)( 1,9 )
C) (3,22)( 3,22 )
D) (9,1)( 9,1 )
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5
Solve graphically.
32x13y=552x+23y=12\begin{array} { l } \frac { 3 } { 2 } x - \frac { 1 } { 3 } y = 5 \\\frac { 5 } { 2 } x + \frac { 2 } { 3 } y = 12\end{array}
 <strong>Solve graphically.  \begin{array} { l } \frac { 3 } { 2 } x - \frac { 1 } { 3 } y = 5 \\ \frac { 5 } { 2 } x + \frac { 2 } { 3 } y = 12 \end{array}    </strong> A)  ( 4 , - 3 )  В)  ( 3,4 )  C)  ( 4,3 )  D)  ( 3,1 )

A) (4,3)( 4 , - 3 )
В) (3,4)( 3,4 )
C) (4,3)( 4,3 )
D) (3,1)( 3,1 )
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6
Classify the system as consistent or inconsistent, and dependent or independent.
3x=y+36x2y=3\begin{array} { l } 3 x = y + 3 \\6 x - 2 y = 3\end{array}

A) Inconsistent and dependent
B) Consistent and independent
C) Inconsistent and independent
D) Consistent and dependent
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7
Classify the system as consistent or inconsistent, and dependent or independent.
x8=yy+2=x\begin{array} { l } x - 8 = y \\y + 2 = x\end{array}

A) Inconsistent and independent
B) Consistent and independent
C) Consistent and dependent
D) Inconsistent and dependent
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8
Classify the system as consistent or inconsistent, and dependent or independent.
x+5y=195x6y=2\begin{array} { c } x + 5 y = 19 \\5 x - 6 y = 2\end{array}

A) Inconsistent and independent
B) Consistent and independent
C) Consistent and dependent
D) Inconsistent and dependent
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9
Solve graphically.
2x+y=64x+2y=12\begin{array}{l}2 x+y=6 \\4 x+2 y=12\end{array}
 <strong>Solve graphically.  \begin{array}{l} 2 x+y=6 \\ 4 x+2 y=12 \end{array}   </strong> A) No solution B) Infinite number of solutions C)  ( 0,6 )  D)  ( 5 , - 4 )

A) No solution
B) Infinite number of solutions
C) (0,6)( 0,6 )
D) (5,4)( 5 , - 4 )
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10
Solve using the substitution method.
x+y=16y=3x+4\begin{array} { l } x + y = 16 \\y = 3 x + 4\end{array}

A) (4,12)( 4,12 )
B) (2,16)( 2,16 )
C) (3,13)( 3,13 )
D) (13,3)( 13,3 )
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11
Solve graphically.
x=yy+x=6\begin{array}{l}x=-y \\y+x=6\end{array}
 <strong>Solve graphically.  \begin{array}{l} x=-y \\ y+x=6 \end{array}   </strong> A)  ( 1,5 )  B) No solution C)  ( 1,1 )  D) Infinite number of solutions

A) (1,5)( 1,5 )
B) No solution
C) (1,1)( 1,1 )
D) Infinite number of solutions
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12
Classify the system as consistent or inconsistent, and dependent or independent.
10x2y=105xy=5\begin{array} { c } - 10 x - 2 y = 10 \\5 x - y = - 5\end{array}

A) Consistent and independent
B) Inconsistent and independent
C) Inconsistent and dependent
D) Consistent and dependent
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13
Solve graphically.
3x+2y=56x4y=5\begin{array}{c}3 x+2 y=5 \\-6 x-4 y=5\end{array}
 <strong>Solve graphically.  \begin{array}{c} 3 x+2 y=5 \\ -6 x-4 y=5 \end{array}   </strong> A)  ( 1.5 , - 1 )  B) No solution C)  ( 1,1 )  D)  ( - 1.5 , - 1 )

A) (1.5,1)( 1.5 , - 1 )
B) No solution
C) (1,1)( 1,1 )
D) (1.5,1)( - 1.5 , - 1 )
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14
Classify the system as consistent or inconsistent, and dependent or independent.
x+6y=172x+12y=34\begin{array} { c } x + 6 y = 17 \\2 x + 12 y = 34\end{array}

A) Inconsistent and dependent
B) Consistent and dependent
C) Inconsistent and independent
D) Consistent and independent
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15
Solve using the substitution method.
y=2x44x+y=28\begin{array} { l } y = 2 x - 4 \\4 x + y = - 28\end{array}

A) (5,14)( - 5 , - 14 )
В) (12,4)( - 12 , - 4 )
C) (12,20)( - 12,20 )
D) (4,12)( - 4 , - 12 )
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16
Solve graphically.
3x2y=46x+4y=7\begin{array}{c}3 x-2 y=4 \\-6 x+4 y=7\end{array}
 <strong>Solve graphically.  \begin{array}{c} 3 x-2 y=4 \\ -6 x+4 y=7 \end{array}   </strong> A) Infinite number of solutions B)  ( 2,1 )  C) No solution D)  ( 1,2 )

A) Infinite number of solutions
B) (2,1)( 2,1 )
C) No solution
D) (1,2)( 1,2 )
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17
Classify the system as consistent or inconsistent, and dependent or independent.
4x+4y=18x+8y=2\begin{array} { l } 4 x + 4 y = 1 \\8 x + 8 y = 2\end{array}

A) Inconsistent and dependent
B) Consistent and dependent
C) Inconsistent and independent
D) Consistent and independent
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18
Classify the system as consistent or inconsistent, and dependent or independent.
x+y=82x2y=8\begin{array} { c } x + y = 8 \\2 x - 2 y = 8\end{array}

A) Inconsistent and dependent
B) Consistent and dependent
C) Consistent and independent
D) Inconsistent and independent
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19
Solve graphically.
x=2y=1\begin{array} { l } x = - 2 \\y = 1\end{array}
 <strong>Solve graphically.  \begin{array} { l } x = - 2 \\ y = 1 \end{array}    </strong> A) Infinitely many solutions B) No solution C)  ( - 2,1 )  D)  ( 1 , - 2 )

A) Infinitely many solutions
B) No solution
C) (2,1)( - 2,1 )
D) (1,2)( 1 , - 2 )
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20
Classify the system as consistent or inconsistent, and dependent or independent.
x3y=63y+1=x\begin{array} { r } x - 3 y = 6 \\3 y + 1 = x\end{array}

A) Consistent and independent
B) Inconsistent and independent
C) Consistent and dependent
D) Inconsistent and dependent
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21
Solve using the elimination method.
x+y=11x + y = 11 xy=7x - y = 7

A) No solution
B) (9,2)( 9,2 )
C) (8,3)( 8,3 )
D) (9,3)( - 9,3 )
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22
Solve by the substitution method.
x+y=75x+5y=35\begin{array} { c } x + y = 7 \\5 x + 5 y = 35\end{array}

A) (0,0)( 0,0 )
B) Infinite number of solutions
C) (7,5)( 7,5 )
D) (8,1)( 8 , - 1 )
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23
Solve by the substitution method.
x5y=276x6y=90\begin{array} { l } x - 5 y = - 27 \\- 6 x - 6 y = - 90\end{array}

A) No solution
В) (8,8)( - 8,8 )
C) (7,8)( 7,8 )
D) (8,7)( 8,7 )
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24
Solve the problem.
The sum of two numbers is 34 and their difference is 12. Find the numbers.

A)23 and 11
B)25 and 37
C)9 and 25
D)11 and 23
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25
Solve by the substitution method.
x+y=1x+y=4\begin{array} { l } x + y = - 1 \\x + y = 4\end{array}

A) (0,3)( 0,3 )
B) No solution
C) (0,0)( 0,0 )
D) (1,4)( - 1,4 )
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26
Solve by the substitution method.
x+6y=17x+7y=7\begin{array} { l } x + 6 y = - 1 \\7 x + 7 y = - 7\end{array}

A) (1,0)( - 1,0 )
B) (0,1)( 0 , - 1 )
C) (1,1)( 1 , - 1 )
D) No solution
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27
Solve using the elimination method.
4xy=195x+y=35\begin{array} { l } 4 x - y = 19 \\5 x + y = 35\end{array}

A) (5,6)( 5,6 )
B) (6,5)( 6,5 )
C) (6,6)( 6,6 )
D) No solution
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28
Solve the problem.
The perimeter of a rectangle is 78 m78 \mathrm {~m} . If the width were doubled and the length were increased by 12 m12 \mathrm {~m} , the perimeter would be 132 m132 \mathrm {~m} . What are the length and width of the rectangle?

A) width 19 m19 \mathrm {~m} , length 19 m19 \mathrm {~m}
B) width 14 m14 \mathrm {~m} , length 19 m19 \mathrm {~m}
C) width 15 m15 \mathrm {~m} , length 24 m24 \mathrm {~m}
D) width 24 m24 \mathrm {~m} , length 15 m15 \mathrm {~m}
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29
Solve using the substitution method.
x=1+2yx+2y=8\begin{array} { l } x = 1 + - 2 y \\x + 2 y = 8\end{array}

A) Infinitely many solutions
B) (7,15)( - 7,15 )
C) (7,15)( - 7 , - 15 )
D) No solution
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30
Solve by the substitution method.
8x+8y=325x4y=20\begin{array} { l } 8 x + 8 y = - 32 \\5 x - 4 y = - 20\end{array}

A) (5,1)( - 5,1 )
B) No solution
C) (4,0)( - 4,0 )
D) (4,1)( - 4,1 )
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31
Solve the problem.
Two angles have a sum of 8181 ^ { \circ } . Their difference is 1515 ^ { \circ } . Find the angles.

A) 6767 ^ { \circ } and 1414 ^ { \circ }
B) 3535 ^ { \circ } and 5050 ^ { \circ }
C) 4848 ^ { \circ } and 3333 ^ { \circ }
D) 4646 ^ { \circ } and 3535 ^ { \circ }
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32
Solve the problem.
The perimeter of a triangle is 65 cm65 \mathrm {~cm} . The triangle is isosceles now, but if its base were lengthened by 6 cm6 \mathrm {~cm} and each leg were shortened by 7 cm7 \mathrm {~cm} , it would be equilateral. Find the base of the original triangle.

A) 19 cm19 \mathrm {~cm}
B) 26 cm26 \mathrm {~cm}
C) 13 cm13 \mathrm {~cm}
D) 12 cm12 \mathrm {~cm}
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33
Solve the problem.
The perimeter of a rectangle is 56 cm56 \mathrm {~cm} . One side is 12 cm12 \mathrm {~cm} longer than the other side. Find the lengths of the sides.

A) 8 cm,20 cm8 \mathrm {~cm} , 20 \mathrm {~cm}
B) 11 cm,23 cm11 \mathrm {~cm} , 23 \mathrm {~cm}
C) 8 cm,12 cm8 \mathrm {~cm} , 12 \mathrm {~cm}
D) 16 cm,28 cm16 \mathrm {~cm} , 28 \mathrm {~cm}
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34
Solve by the substitution method.
7x+9y=543x4y=24\begin{array} { c } 7 x + 9 y = - 54 \\- 3 x - 4 y = 24\end{array}

A) (1,5)( - 1 , - 5 )
B) (0,5)( 0 , - 5 )
C) No solution
D) (0,6)( 0 , - 6 )
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35
Solve by the substitution method.
6x+9y=1144x4y=4\begin{array} { l } 6 x + 9 y = 114 \\4 x - 4 y = - 4\end{array}

A) No solution
B) (7,9)( 7,9 )
C) (6,9)( 6,9 )
D) (7,8)( 7,8 )
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36
Solve by the substitution method.
x+3y=187x+4y=24\begin{array} { r } x + 3 y = 18 \\7 x + 4 y = 24\end{array}

A) (0,6)( 0,6 )
B) No solution
C) (6,0)( - 6,0 )
D) (1,5)( 1,5 )
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37
Solve the problem.
Find two numbers whose sum is 40 and whose difference is 12.

A)29 and 11
B)26 and 14
C)24 and 16
D)16 and 28
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38
Solve using the elimination method.
x3y=25x+3y=46\begin{array} { l } - x - 3 y = - 2 \\- 5 x + 3 y = - 46\end{array}

A) (8,2)( 8 , - 2 )
B) No solution
C) (9,3)( 9 , - 3 )
D) (2,8)( 2,8 )
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39
Solve the problem.
The sum of two angles is 225225 ^ { \circ } . One angle is 3030 ^ { \circ } less than twice the other. Find the angles.

A) 136136 ^ { \circ } and 8989 ^ { \circ }
B) 8585 ^ { \circ } and 140140 ^ { \circ }
C) 8383 ^ { \circ } and 142142 ^ { \circ }
D) 8383 ^ { \circ } and 136136 ^ { \circ }
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40
Solve by the substitution method.
8x+17=9y6x2y=4\begin{array} { l } 8 x + 17 = 9 y \\- 6 x - 2 y = 4\end{array}

A) (1,2)( - 1,2 )
B) No solution
C) (2,2)( - 2,2 )
D) (1,1)( - 1,1 )
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41
Solve the problem using the elimination method.
Two angles are supplementary, and one is 4040 ^ { \circ } more than three times the other. Find the smaller angle.

A) 145145 ^ { \circ }
B) 105105 ^ { \circ }
C) 7575 ^ { \circ }
D) 3535 ^ { \circ }
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42
Solve the system of equations by the elimination method.
32x13y=1834x+29y=9\begin{array} { l } \frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 18 \\\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 9\end{array}

A) (12,0)( - 12,0 )
B) (0,12)( 0 , - 12 )
C) (0,12)( 0,12 )
D) (12,0)( 12,0 )
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43
Solve the system of equations by the elimination method.
x+5y=24x+6y=8\begin{array} { c } x + 5 y = 2 \\- 4 x + 6 y = - 8\end{array}

A) (2,0)( 2,0 )
B) no solution
C) (3,2)( 3,2 )
D) (2,1)( - 2 , - 1 )
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44
Solve the problem using the elimination method.
There were 490 people at a play. The admission price was $3\$ 3 for adults and $1\$ 1 for children. The admission receipts were $1070\$ 1070 . How many adults and how many children attended?

A) 290 adults and 200 children
B) 267 adults and 223 children
C) 100 adults and 390 children
D) 200 adults and 290 children
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45
Solve the system of equations by the elimination method.
5x6y=515x18y=15\begin{array} { l } 5 x - 6 y = - 5 \\15 x - 18 y = 15\end{array}

A) no solution
B) (25,30)( 25 , - 30 )
C) infinitely many solutions
D) (25,30)( - 25,30 )
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46
Solve the problem using the elimination method.
Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $81\$ 81 for 3 days and 300 miles, while Mary was charged $145\$ 145 for 5 days and 600 miles. What does Best Rental charge per day and per mile?

A) $18\$ 18 per day and 1111 \nsubseteq per mile
B) $10\$ 10 per day and 17517 \nsubseteq 5 per mile
C) $16\$ 16 per day and 1111 \nsubseteq \subset per mile
D) $17\$ 17 per day and 1010 \simeq per mile
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47
Solve the system of equations by the elimination method.
7x6y=363x+4y=24\begin{array} { l } - 7 x - 6 y = - 36 \\- 3 x + 4 y = 24\end{array}

A) no solution
B) (0,7)( 0,7 )
C) (0,6)( 0,6 )
D) (1,7)( - 1,7 )
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48
Solve the system of equations by the elimination method.
0.3x+0.5y=3.1x0.1y=1.5\begin{array} { r } 0.3 x + 0.5 y = 3.1 \\x - 0.1 y = 1.5\end{array}

A) (0.2,0.5)( 0.2,0.5 )
B) (5,2)( 5,2 )
C) no solution
D) (2,5)( 2,5 )
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49
Solve the system of equations by the elimination method.
x+3y=156x+4y=20\begin{array} { c } x + 3 y = 15 \\- 6 x + 4 y = 20\end{array}

A) no solution
B) (1,4)( 1,4 )
C) (5,0)( - 5,0 )
D) (0,5)( 0,5 )
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50
Solve using the elimination method.
x+6y=262x+6y=22\begin{array} { c } x + 6 y = 26 \\2 x + 6 y = 22\end{array}

A) (4,4)( 4,4 )
B) No solution
C) (4,5)( - 4,5 )
D) (3,4)( - 3 , - 4 )
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51
Solve the system of equations by the elimination method.
3x5y=218x30y=12\begin{array} { l } 3 x - 5 y = 2 \\18 x - 30 y = 12\end{array}

A) (6,10)( 6 , - 10 )
B) infinitely many solutions
C) (10,6)( - 10,6 )
D) no solution
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52
Solve the system of equations by the elimination method.
9x+9y=454x6y=20\begin{array} { l } 9 x + 9 y = - 45 \\- 4 x - 6 y = 20\end{array}

A) (5,1)( - 5,1 )
B) no solution
C) (5,0)( - 5,0 )
D) (6,1)( - 6,1 )
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53
Solve the problem using the elimination method.
A salesman sold $200\$ 200 more than the rest of the sales staff. If the sales total for the day was $2050\$ 2050 , how much did the rest of the sales staff sell?

A) $1125\$ 1125
B) $925\$ 925
C) $1850\$ 1850
D) $1025\$ 1025
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54
Solve the problem using the elimination method.
In a right triangle, one acute angle is 5454 ^ { \circ } more than twice the other. Find each acute angle.

A) 1212 ^ { \circ } and 7878 ^ { \circ }
B) 3737 ^ { \circ } and 5353 ^ { \circ }
C) 2121 ^ { \circ } and 6969 ^ { \circ }
D) 2828 ^ { \circ } and 6262 ^ { \circ }
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55
Solve the system of equations by the elimination method.
32x13y=21\frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 21
34x+29y=7\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 7

A) (12,9)( - 12,9 )
В) (12,9)( 12,9 )
C) (12,9)( - 12 , - 9 )
D) (9,12)( 9 , - 12 )
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56
Solve the problem using the elimination method.
There were 38,000 people at a ball game in Los Angeles. The day's receipts were $229,000\$ 229,000 . How many people paid $11\$ 11 for reserved seats and how many paid $4\$ 4 for general admission?

A) 19,250 paid $11\$ 11 and 18,750 paid $4\$ 4
B) 27,000 paid $11\$ 11 and 11,000 paid $4\$ 4
C) 18,750 paid $11\$ 11 and 19,250 paid $4\$ 4
D) 11,000 paid $11\$ 11 and 27,000 paid $4\$ 4
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57
Solve the problem using the elimination method.
Two angles are supplementary, and one is 55 ^ { \circ } more than six times the other. Find the larger angle.

A) 2525 ^ { \circ }
B) 155155 ^ { \circ }
C) 7070 ^ { \circ }
D) 110110 ^ { \circ }
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58
Solve the system of equations by the elimination method.
0.8x+0.4y=4.8- 0.8 x + 0.4 y = 4.8 0.1x0.1y=0.70.1 x - 0.1 y = - 0.7

A) (50,20)( - 50,20 )
В) (0.5,0.2)( - 0.5,0.2 )
C) (5,2)( - 5,2 )
D) (2,5)( 2 , - 5 )
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59
Solve the system of equations by the elimination method.
2.5x+0.3y=10.60.5x+0.9y=3.8\begin{array} { l } 2.5 x + 0.3 y = 10.6 \\0.5 x + 0.9 y = 3.8\end{array}

A) (6.5,2.3)( 6.5,2.3 )
B) (4,2)( 4,2 )
C) (4.5,2)( 4.5,2 )
D) (1.5,2.3)( 1.5,2.3 )
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60
Solve the system of equations by the elimination method.
x3y=54x4y=12\begin{array} { c } x - 3 y = - 5 \\4 x - 4 y = 12\end{array}
4x4y=124 \mathrm { x } - 4 \mathrm { y } = 12

A) (7,4)( 7,4 )
В) (6,5)( 6,5 )
C) no solution
D) (7,5)( - 7,5 )
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61
Solve the problem using the elimination method.
The sum of two numbers is 100 . The second number is three times as large as the first number. What are the numbers?

A) 22 and 78
B) 23 and 69
C) 23 and 77
D) 25 and 75
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62
Solve the problem.
A merchant has coffee worth $20\$ 20 a pound that she wishes to mix with 90 pounds of coffee worth $90\$ 90 a pound to get a mixture that can be sold for $80\$ 80 a pound. How many pounds of the $20\$ 20 coffee should be used?

A) 7.5lb7.5 \mathrm { lb }
B) 52.5lb52.5 \mathrm { lb }
C) 105lb105 \mathrm { lb }
D) 15lb15 \mathrm { lb }
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63
Solve the problem.
There were 670 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $1020. How many adults and how many children attended?

A)320 adults and 350 children
B)255 adults and 415 children
C)350 adults and 320 children
D)160 adults and 510 children
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64
Solve the problem.
Anne and Nancy use a metal alloy that is 16%16 \% copper to make jewelry. How many ounces of an alloy that is 10%10 \% copper must be mixed with an alloy that is 20%20 \% copper to form 55 ounces of the desired alloy?

A) 22 ounces
B) 33 ounces
C) 38 ounces
D) 24 ounces
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65
Solve the problem.
Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 28 coins with a total face value of $5.00\$ 5.00 , how many of the coins are nickels?

A) 23 nickels
B) 10 nickels
C) 12 nickels
D) 18 nickels
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66
Solve the problem.
Walt made an extra $10,000\$ 10,000 last year from a part-time job. He invested part of the money at 10%10 \% and the rest at 9%9 \% . He made a total of $960\$ 960 in interest. How much was invested at 9%9 \% ?

A) $8000\$ 8000
B) $5000\$ 5000
C) $6000\$ 6000
D) $4000\$ 4000
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67
Solve the problem.
Andy has 33 coins made up of quarters and half dollars, and their total value is $13.25\$ 13.25 . How many quarters does he have?

A) 18 quarters
B) 22 quarters
C) 20 quarters
D) 13 quarters
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68
Solve the problem.
Ellen wishes to mix candy worth $1.79\$ 1.79 per pound with candy worth $3.75\$ 3.75 per pound to form 22 pounds of a mixture worth $2.95\$ 2.95 per pound. How many pounds of the more expensive candy should she use?

A) 13 pounds
B) 11 pounds
C) 9 pounds
D) 18 pounds
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69
Solve the problem.
Mardi received an inheritance of $60,000\$ 60,000 . She invested part at 8%8 \% and deposited the remainder in tax-free bonds at 11%11 \% . Her total annual income from the investments was $5700\$ 5700 . Find the amount invested at 8%8 \% .

A) $54,300\$ 54,300
B) $29,000\$ 29,000
C) $30,000\$ 30,000
D) $15,000\$ 15,000
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70
Solve the problem.
A sum of money amounting to $3.45\$ 3.45 consists of dimes and quarters. If there are 18 coins in all, how many are quarters?

A) 16 quarters
B) 7 quarters
C) 11 quarters
D) 9 quarters
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71
Solve the problem.
How many liters of a 20%20 \% alcohol solution must be mixed with 90 liters of a 80%80 \% solution to get a 40%40 \% solution?

A) 27 L27 \mathrm {~L}
B) 18 L18 \mathrm {~L}
C) 180 L180 \mathrm {~L}
D) 270 L270 \mathrm {~L}
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72
Solve the problem using the elimination method.
The sum of two numbers is 41 . The larger number minus the smaller number is 9 . What are the numbers?

A) 18 and 27
B) 25 and 16
C) 33 and 8
D) 23 and 18
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73
Solve the problem.
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 28 pounds of feed worth $0.62\$ 0.62 per pound by mixing one kind worth $0.15\$ 0.15 per pound with another worth $0.97\$ 0.97 per pound. How many pounds of the cheaper kind should they use in the mix?

A) 21 pounds
B) 14 pounds
C) 12 pounds
D) 16 pounds
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74
Solve the problem.
A woman made a deposit of $267. If her deposit consisted of 91 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

A)44 one-dollars
B)42 one-dollars
C)37 one-dollars
D)47 one-dollars
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75
Solve the problem.
In a chemistry class, 6 liters of a 4%4 \% silver iodide solution must be mixed with a 10%10 \% solution to get a 6%6 \% solution. How many liters of the 10%10 \% solution are needed?

A) 4.0 L4.0 \mathrm {~L}
B) 3.0 L3.0 \mathrm {~L}
C) 2.0 L2.0 \mathrm {~L}
D) 6.0 L6.0 \mathrm {~L}
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76
Solve the problem using the elimination method.
In a basketball game, Will scored 40 points, consisting only of three-point shots and two-point shots. He made a total of 17 shots. How many shots of each type did he make?

A) two-point shots: 11 ; three-point shots: 6
B) two-point shots: 6; three-point shots: 11
C) two-point shots: 10 ; three-point shots: 7
D) two-point shots: 12; three-point shots: 5
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77
Solve the problem using the elimination method.
A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $5.00\$ 5.00 . Another customer buys 4 hot dogs and 3 bags of potato chips for $9.00\$ 9.00 . Find the cost of each item.

A) $1.75\$ 1.75 for a hot dog; $1.25\$ 1.25 for a bag of potato chips
B) $1.50\$ 1.50 for a hot dog; $1.25\$ 1.25 for a bag of potato chips
C) $1.00\$ 1.00 for a hot dog; $1.50\$ 1.50 for a bag of potato chips
D) $1.50\$ 1.50 for a hot dog; $1.00\$ 1.00 for a bag of potato chips
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78
Solve the problem.
A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 9%9 \% cement should he mix with 10 bags of 10.8%10.8 \% cement to produce a mix containing 10%10 \% cement?

A) 23 bags
B) 10 bags
C) 8 bags
D) 18 bags
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79
Solve the problem.
Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $3.00 each and Kathy selling adult tickets for $5.50 each. If their total income for 25 tickets was $120.00, how many did Ron sell?

A)23 tickets
B)18 tickets
C)7 tickets
D)9 tickets
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80
Solve the problem using the elimination method.
The sum of two numbers is 4 . Three times the larger number plus two times the smaller number is 37 . Find the numbers.

A) 25 and 21- 21
B) 33 and 29- 29
C) 29 and 25- 25
D) 25 and 29- 29
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