Deck 3: Systems of Equations

Question 1

Classify the system as consistent or inconsistent, and dependent or independent.
x + y = -7 x - y = 5

A)Consistent and dependent
B)Inconsistent and independent
C)Consistent and independent
D)Inconsistent and dependent

Answer 1

Consistent and independent

Question 2

Solve graphically.

A)No solution
B)(1, 1)
C)(1, 5)
D)Infinite number of solutions

Answer 2

No solution

Question 3

Solve using the substitution method.
x + y = 1 y = -2x - 3

A)(-3, 6)
B)(-5, 1)
C)(-4, 5)
D)(5, -4)

Answer 3

(-4, 5)

Question 4

Solve graphically.

A)(4, 3)
B)(3, 4)
C)(3, 1)
D)(4, -3)

Question 5

Classify the system as consistent or inconsistent, and dependent or independent.

A)Consistent and dependent
B)Inconsistent and dependent
C)Consistent and independent
D)Inconsistent and independent

Question 6

Solve graphically.

A)(2, 15)
B)No solution
C)(8, 9)
D)(9, 8)

Question 7

Solve graphically.

A)No solution
B)(2, 1)
C)(1, 2)
D)Infinite number of solutions

Question 8

Classify the system as consistent or inconsistent, and dependent or independent.
x + y = -12 2x - 2y = -12

A)Inconsistent and dependent
B)Inconsistent and independent
C)Consistent and independent
D)Consistent and dependent

Question 9

Classify the system as consistent or inconsistent, and dependent or independent.
x + 4y = 16 5x - 2y = 14

A)Consistent and dependent
B)Consistent and independent
C)Inconsistent and independent
D)Inconsistent and dependent

Question 10

Classify the system as consistent or inconsistent, and dependent or independent.
x - 4 = y y + 5 = x

A)Consistent and dependent
B)Consistent and independent
C)Inconsistent and independent
D)Inconsistent and dependent

Question 11

Solve graphically.

A)(1, -4)
B)Infinitely many solutions
C)No solution
D)(-4, 1)

Question 12

Solve graphically.

A)(5, -2)
B)Infinite number of solutions
C)No solution
D)(0, 8)

Question 13

Solve graphically.

A)(-4, -5)
B)(4, 4)
C)(-2, -2)
D)(-4, 4)

Question 14

Solve using the substitution method.
y = 2x + 4 3x + y = 29

A)(5, 14)
B)(14, 5)
C)(14, -13)
D)(4, 12)

Question 15

Solve graphically.

A)No solution
B)(1.5, -1)
C)(-1.5, -1)
D)(1, 1)

Question 16

Classify the system as consistent or inconsistent, and dependent or independent.
x + 2y = 17 2x + 4y = 34

A)Consistent and dependent
B)Inconsistent and dependent
C)Inconsistent and independent
D)Consistent and independent

Question 17

Classify the system as consistent or inconsistent, and dependent or independent.
5x + 4y = 3 10x + 8y = 6

A)Consistent and independent
B)Inconsistent and independent
C)Inconsistent and dependent
D)Consistent and dependent

Question 18

Classify the system as consistent or inconsistent, and dependent or independent.
x - 3y = 6 3y + 1 = x

A)Inconsistent and dependent
B)Inconsistent and independent
C)Consistent and dependent
D)Consistent and independent

Question 19

Classify the system as consistent or inconsistent, and dependent or independent.
10x + 2y = -4 5x - y = -2

A)Inconsistent and dependent
B)Consistent and dependent
C)Consistent and independent
D)Inconsistent and independent

Question 20

Classify the system as consistent or inconsistent, and dependent or independent.
3x = y + 3 6x - 2y = 3

A)Inconsistent and independent
B)Consistent and independent
C)Consistent and dependent
D)Inconsistent and dependent

Question 21

Solve by the substitution method.
x - 4y = -4 7x - 3y = -28

A)(-4, 0)
B)(-3, -4)
C)(4, -1)
D)No solution

Question 22

Solve using the elimination method.
- x - 6y = - 11 3x + 6y = 9

A)(-1, 2)
B)(-2, -1)
C)(0, 1)
D)No solution

Question 23

Solve by the substitution method.
x - 2y = -12 -2x - 3y = -4

A)(-4, 4)
B)(4, 5)
C)(-5, 5)
D)No solution

Question 24

Solve by the substitution method.
x + y = 6 8x + 8y = 48

A)(6, 8)
B)(0, 0)
C)Infinite number of solutions
D)(1, 5)

Question 25

Solve by the substitution method.
x + y = -6 x + y = -4

A)No solution
B)(0, 0)
C)(-6, -4)
D)(0, -10)

Question 26

Solve by the substitution method.
9x - 6y = -72 -2x + 3y = 31

A)No solution
B)(-3, 10)
C)(-2, 9)
D)(-2, 10)

Question 27

Solve by the substitution method.
x - 6y = -6 4x - 5y = -5

A)No solution
B)(-1, 0)
C)(0, 1)
D)(1, 0)

Question 28

Solve by the substitution method.
7x + 7y = -28 -4x - 4y = 16

A)(-5, 1)
B)(-4, 0)
C)No solution
D)(-4, 1)

Question 29

Solve the problem.
The perimeter of a rectangle is 50 m. If the width were doubled and the length were increased by 5 m, the perimeter would be 74 m. What are the length and width of the rectangle?

A)width 7 m, length 12 m
B)width 12 m, length 12 m
C)width 7 m, length 18 m
D)width 18 m, length 7 m

Question 30

Solve by the substitution method.
-7x + 7y = 21 -5x - 2y = -6

A)(0, 4)
B)No solution
C)(0, 3)
D)(-1, 4)

Question 31

Solve using the substitution method.
x = -1 + 8y x + -8y = 3

A)Infinitely many solutions
B)
C)
D)No solution

Question 32

Solve the problem.
The sum of two numbers is 34 and their difference is 8. Find the numbers.

A)15 and 23
B)21 and 13
C)27 and 7
D)19 and 15

Question 33

Solve the problem.
The sum of two angles is 110°. One angle is 25° less than twice the other. Find the angles.

A)43° and 61°
B)45° and 65°
C)61° and 49°
D)43° and 67°

Question 34

Solve the problem.
The perimeter of a triangle is 48 cm. The triangle is isosceles now, but if its base were lengthened by 6 cm and each leg were shortened by 6 cm, it would be equilateral. Find the base of the original triangle.

A)8 cm
B)20 cm
C)14 cm
D)7 cm

Question 35

Solve by the substitution method.
7x + 27 = 8y 5x + 6y = -31

A)No solution
B)(-5, 0)
C)(-6, 0)
D)(-5, -1)

Question 36

Solve the problem.
Find two numbers whose sum is 42 and whose difference is 0.

A)23 and 23
B)21 and 21
C)43 and -1
D)19 and 23

Question 37

Solve using the elimination method.
x + y = 6 x - y = 12

A)(8, -2)
B)(-9, -2)
C)(9, -3)
D)No solution

Question 38

Solve using the elimination method.
4 x - y = 20 3x + y = 22

A)No solution
B)(6, 5)
C)(4, 6)
D)(6, 4)

Question 39

Solve the problem.
The perimeter of a rectangle is 60 cm. One side is 12 cm longer than the other side. Find the lengths of the sides.

A)11 cm, 23 cm
B)9 cm, 12 cm
C)18 cm, 30 cm
D)9 cm, 21 cm

Question 40

Solve the problem.
Two angles have a sum of 108°. Their difference is 6°. Find the angles.

A)53° and 59°
B)103° and 5°
C)55° and 53°
D)57° and 51°

Question 41

Solve the system of equations by the elimination method.
3x - 6y = -3 -6x + 12y = 6

A)infinitely many solutions
B)(18, -9)
C)no solution
D)(-9, 18)

Question 42

Solve the system of equations by the elimination method.
-0.1x + 0.6y = -3.2 0.7x - 0.1y = -2.2

A)(-0.4, -0.6)
B)(-40, -60)
C)(-4, -6)
D)(-6, -4)

Question 43

Solve the system of equations by the elimination method.

A)(0, 12)
B)(-12, 0)
C)(12, 0)
D)(0, -12)

Question 44

Solve the problem using the elimination method.
Two angles are supplementary, and one is 5° more than six times the other. Find the larger angle.

A)155°
B)110°
C)25°
D)70°

Question 45

Solve the problem using the elimination method.
There were 41,000 people at a ball game in Los Angeles. The day's receipts were $322,000. How many people paid $14 for reserved seats and how many paid $5 for general admission?

A)11,750 paid $14 and 29,250 paid $5
B)13,000 paid $14 and 28,000 paid $5
C)28,000 paid $14 and 13,000 paid $5
D)29,250 paid $14 and 11,750 paid $5

Question 46

Solve the system of equations by the elimination method.
x - 3y = -24 5x - 2y = -16

A)(-8, 0)
B)(1, 7)
C)(0, 8)
D)no solution

Question 47

Solve the system of equations by the elimination method.
x - 3y = -4 7x - 2y = -28

A)(-4, 0)
B)(4, -1)
C)no solution
D)(-3, -4)

Question 48

Solve the system of equations by the elimination method.

A)(-12, -9)
B)(9, -12)
C)(12, 9)
D)(-12, 9)

Question 49

Solve using the elimination method.
x + 9y = -15 2x + 9y = -12

A)(4, 3)
B)No solution
C)(-3, -3)
D)(3, -2)

Question 50

Solve the system of equations by the elimination method.
-5x + 8y = 56 -3x + 4y = 28

A)(0, 8)
B)(0, 7)
C)(-1, 8)
D)no solution

Question 51

Solve the problem using the elimination method.
In a right triangle, one acute angle is 54° more than twice the other. Find each acute angle.

A)28° and 62°
B)37° and 53°
C)21° and 69°
D)12° and 78°

Question 52

Solve the problem using the elimination method.
There were 470 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $720. How many adults and how many children attended?

A)110 adults and 360 children
B)220 adults and 250 children
C)250 adults and 220 children
D)180 adults and 290 children

Question 53

Solve the system of equations by the elimination method.
-2x - 4y = 6 -4x - 8y = -12

A)infinitely many solutions
B)no solution
C)(-12, -24)
D)(12, 24)

Question 54

Solve the system of equations by the elimination method.
2.8x + 0.4y = 12.4 0.7x + 0.8y = 5.2

A)(1.2, 3.4)
B)(4.9, 3)
C)(6.8, 3.4)
D)(4, 3)

Question 55

Solve the system of equations by the elimination method.
7x + 8y = 7 -4x - 4y = -4

A)(0, 1)
B)no solution
C)(1, 1)
D)(1, 0)

Question 56

Solve the problem using the elimination method.
A salesman sold $100 more than the rest of the sales staff. If the sales total for the day was $2250, how much did the rest of the sales staff sell?

A)$1125
B)$1175
C)$1075
D)$2150

Question 57

Solve the problem using the elimination method.
Two angles are supplementary, and one is 40° more than three times the other. Find the smaller angle.

A)105°
B)75°
C)35°
D)145°

Question 58

Solve the system of equations by the elimination method.
0.4x + 0.2y = 0.4 x - 0.3y = -2.2

A)(-0.1, 0.4)
B)(4, -1)
C)no solution
D)(-1, 4)

Question 59

Solve the system of equations by the elimination method.
x + 9y = -42 3x + 8y = -50

A)(-7, -3)
B)(6, -3)
C)no solution
D)(-6, -4)

Question 60

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 for 3 days and 300 miles, while Mary was charged $145 for 5 days and 600 miles. What does Best Rental charge per day and
Per mile?

A)$17 per day and per mile
B)$10 per day and per mile
C)$16 per day and per mile
D)$18 per day and per mile

Question 61

Solve the problem.
In a chemistry class, 3 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

A)3.0 L
B)2.5 L
C)0.5 L
D)1.5 L

Question 62

Solve the problem.
Ellen wishes to mix candy worth $1.08 per pound with candy worth $3.05 per pound to form 24 pounds of a mixture worth $2.64 per pound. How many pounds of the more expensive candy should she use?

A)24 pounds
B)7 pounds
C)19 pounds
D)5 pounds

Question 63

Solve the problem.
Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 13 coins with a total face value of $2.25, how many of the coins are nickels?

A)7 nickels
B)8 nickels
C)5 nickels
D)13 nickels

Question 64

Solve the problem.
A sum of money amounting to $5.50 consists of dimes and quarters. If there are 31 coins in all, how many are quarters?

A)15 quarters
B)21 quarters
C)17 quarters
D)16 quarters

Question 65

Solve the problem.
There were 630 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $960. How many adults and how many children attended?

A)300 adults and 330 children
B)330 adults and 300 children
C)150 adults and 480 children
D)240 adults and 390 children

Question 66

Solve the problem.
Walt made an extra $5000 last year from a part-time job. He invested part of the money at 6% and the rest at 9%. He made a total of $420 in interest. How much was invested at 9%?

A)$4000
B)$2500
C)$3000
D)$1000

Question 67

Solve the problem.
Andy has 23 coins made up of quarters and half dollars, and their total value is $7.75. How many quarters does he have?

A)15 quarters
B)20 quarters
C)10 quarters
D)8 quarters

Question 68

Solve the problem.
How many liters of a 20% alcohol solution must be mixed with 90 liters of a 90% solution to get a 30% solution?

A)63 L
B)630 L
C)54 L
D)540 L

Question 69

Solve the problem.
A merchant has coffee worth $20 a pound that she wishes to mix with 80 pounds of coffee worth $80 a pound to get a mixture that can be sold for $60 a pound. How many pounds of the $20 coffee should be used?

A)40 lb
B)60 lb
C)20 lb
D)120 lb

Question 70

Solve the problem.
Anne and Nancy use a metal alloy that is 17% copper to make jewelry. How many ounces of an alloy that is 11% copper must be mixed with an alloy that is 22% copper to form 55 ounces of the desired alloy?

A)25 ounces
B)30 ounces
C)35 ounces
D)27 ounces

Question 71

Solve the problem.
Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $2.00 each and Kathy selling adult tickets for $6.50 each. If their total income for 22 tickets was $102.50, how many did Ron sell?

A)13 tickets
B)9 tickets
C)18 tickets
D)11 tickets

Question 72

Solve the problem.
A woman made a deposit of $215. If her deposit consisted of 79 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

A)35 one-dollars
B)34 one-dollars
C)45 one-dollars
D)40 one-dollars

Question 73

Solve the problem.
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 26 pounds of feed worth $0.54 per pound by mixing one kind worth $0.34 per pound with another worth $0.99 per pound. How many pounds of
The cheaper kind should they use in the mix?

A)13 pounds
B)18 pounds
C)8 pounds
D)20 pounds

Question 74

Solve the problem using the elimination method.
The sum of two numbers is 104. The second number is three times as large as the first number. What are the numbers?

A)26 and 78
B)23 and 81
C)24 and 72
D)24 and 80

Question 75

Solve the problem using the elimination method.
The sum of two numbers is 28. The larger number minus the smaller number is 8. What are the numbers?

A)16 and 12
B)21 and 7
C)18 and 10
D)12 and 20

Question 76

Solve the problem.
A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 6% cement should he mix with 4 bags of 19.5% cement to produce a mix containing 9% cement?

A)23 bags
B)18 bags
C)14 bags
D)16 bags

Question 77

Solve the problem.
Mardi received an inheritance of $70,000. She invested part at 11% and deposited the remainder in tax-free bonds at 7%. Her total annual income from the investments was $6900. Find the amount invested at 11%.

A)$50,000
B)$63,100
C)$25,000
D)$49,000

Question 78

Solve the problem using the elimination method.
In a basketball game, Will scored 36 points, consisting only of three-point shots and two-point shots. He made a total of 15 shots. How many shots of each type did he make?

A)two-point shots: 8; three-point shots: 7
B)two-point shots: 6; three-point shots: 9
C)two-point shots: 10; three-point shots: 5
D)two-point shots: 9; three-point shots: 6

Question 79

Solve the problem using the elimination method.
The sum of two numbers is 8. Four times the larger number plus two times the smaller number is 66. Find the numbers.

A)17 and -9
B)17 and -25
C)25 and -17
D)33 and -25

Question 80

Solve the problem using the elimination method.
A vendor sells hot dogs and bags of potato chips. A customer buys 3 hot dogs and 5 bags of potato chips for $9.50. Another customer buys 2 hot dogs and 5 bags of potato chips for $8.00. Find the cost of each item.

A)$1.75 for a hot dog; $1.25 for a bag of potato chips
B)$1.00 for a hot dog; $1.50 for a bag of potato chips
C)$1.50 for a hot dog; $1.00 for a bag of potato chips
D)$1.50 for a hot dog; $1.25 for a bag of potato chips