Question 1

Solve the system of equations by the elimination method.
-x + 8y = 8 
6x + 9y = 48
A)(8, 0)
B)(-8, -1)
C)no solution
D)(9, 8)

Accepted Answer

Multiply the first equation by -6 and add it to the second equation to eliminate x.-6(x + 8y = 8) -> -6x - 48y = -486x + 9y = 48------------------39y = 0y = 0Substitute y = 0 into the first equation to solve for x.x + 8(0) = 8x = 8The solution to the system of equations is (8, 0).

Question 2

Solve the system of equations by the elimination method.
-$\begin{array} { l } 
\frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 18 \
\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 9
\end{array}$
A) $( - 12,0 )$
B) $( 12,0 )$
C) $( 0 , - 12 )$
D) $( 0,12 )$

Accepted Answer

To solve the system of equations by the elimination method, we first make the coefficients of either $x$ or $y$ the same in both equations. Multiplying the second equation by 2 gives us equivalent coefficients for $x$:1. $ \frac{3}{2}x - \frac{1}{3}y = -18 $2. $ \frac{3}{2}x + \frac{4}{9}y = -18 $Subtracting the second equation from the first eliminates $x$, but to simplify the process and avoid mistakes, let's correct the approach by directly aiming to eliminate one variable with initial equations:1. $ \frac{3}{2}x - \frac{1}{3}y = -18 $ (Equation 1)2. $ \frac{3}{4}x + \frac{2}{9}y = -9 $ (Equation 2)To eliminate $y$, we can multiply the first equation by 9 and the second by 3 to get common denominators:1. $ 9(\frac{3}{2}x) - 9(\frac{1}{3}y) = 9(-18) $ => $ \frac{27}{2}x - 3y = -162 $2. $ 3(\frac{3}{4}x) + 3(\frac{2}{9}y) = 3(-9) $ => $ \frac{9}{4}x + \frac{2}{3}y = -27 $To eliminate $y$, we can further adjust the equations to have the same coefficient for $y$, but it seems there was a mistake in the process described. The correct approach to solve it involves directly finding a common coefficient for either $x$ or $y$ and then subtracting or adding the equations. Let's correct the approach:To directly solve it, we can multiply the entire first equation by 2 and the second by 3 to get:1. $3x - \frac{2}{3}y = -36$2. $ \frac{9}{4}x + \frac{2}{3}y = -27$Multiplying the second original equation by 4 gives:1. $3x - \frac{2}{3}y = -36$2. $3x + \frac{8}{9}y = -36$However, the correct elimination process involves finding a least common multiple for coefficients and correctly applying elimination. My initial explanation contained errors in the calculation process. The correct method involves adjusting the coefficients properly and then adding or subtracting the equations to eliminate one variable. Solving it correctly, you would find that $x = -12$ and substituting back to find $y = 0$, which matches choice A.

Question 3

Solve the system of equations by the elimination method.
--4x + 4y = 6 
12x - 12y = 18
A)(-24, 24)
B)infinitely many solutions
C)no solution
D)(24, -24)

Accepted Answer

The two equations are multiples of each other, meaning they represent parallel lines with no intersection, hence no solution.

Question 4

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)25°
C)70°
D)110°

Accepted Answer

The two angles are supplementary, meaning their sum is 180°. Let x be the smaller angle, then the larger angle is 6x + 5°. The equation is x + (6x + 5) = 180. Solving for x gives x = 25°, making the larger angle 6(25) + 5 = 155°.

Question 5

Solve the system of equations by the elimination method.
-0.8x + 0.3y = 10.7 
-0.3x - 0.1y = -3.9
A)(100, 90)
B)(1, 0.9)
C)(10, 9)
D)(9, 10)

Accepted Answer

To eliminate y, multiply the first equation by 1 and the second equation by 3 to get:  0.8x + 0.3y = 10.7  -0.9x - 0.3y = -11.7  Add the equations:  -0.1x = -1  x = 10  Substitute x = 10 into the first equation:  0.8(10) + 0.3y = 10.7  8 + 0.3y = 10.7  0.3y = 2.7  y = 9  The solution is (10, 9).

Question 6

Solve the system of equations by the elimination method.
-9x + 7y = 49 
-3x - 5y = -35
A)(0, 8)
B)no solution
C)(0, 7)
D)(-1, 8)

Accepted Answer

Multiplying the second equation by 3 to eliminate x: 9x + 7y = 49 and -9x - 15y = -105. Adding these equations gives -8y = -56, so y = 7. Substituting y = 7 into the first equation gives 9x + 49 = 49, so x = 0. Therefore, the solution is (0, 7).

Question 7

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 $144 for 5 days and 600 miles. What does Best Rental charge per day and
Per mile? 
A) $\$ 9 \text { per day and } 18 \not \subset \text { per mile }$

B)  $\$ 19 \text { per day and } 10 \not \subset \text { per mile }$

C)  $\$18 \text { per day and } 9 \not \subset \text { per mile }$

D)  $\$ 17 \text { per day and } 10 \not \subset \text { per mile }$

Accepted Answer

By setting up the equations based on the given charges: 3d + 300m = 81 and 5d + 600m = 144, and using elimination, we find the daily charge is $18 and the mileage charge is $9.

Question 8

Solve the problem using the elimination method.
-There were 380 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $600. How many adults and how many children attended?
A)150 adults and 230 children
B)80 adults and 300 children
C)160 adults and 220 children
D)220 adults and 160 children

Accepted Answer

To solve this problem using the elimination method, we set up two equations based on the information given. Let $A$ represent the number of adults and $C$ represent the number of children. We have:1. $A + C = 380$ (since there were 380 people at the play)2. $2A + 1C = 600$ (since the admission receipts were $600, with adults paying $2 and children $1)To use the elimination method, we can multiply the first equation by -1 to make it easier to eliminate one of the variables when we add the two equations together. This gives us:- $A + C = 380$ becomes $-A - C = -380$Adding this to the second equation:- $(-A - C) + (2A + C) = -380 + 600$- $A = 220$Substituting $A = 220$ into the first equation:- $220 + C = 380$- $C = 160$Therefore, there were 220 adults and 160 children at the play.

Question 9

Solve the system of equations by the elimination method.
--7x + 9y = 28 
-3x - 3y = 12
A)no solution
B)(-4, 1)
C)(-5, 1)
D)(-4, 0)

Accepted Answer

The answer of Solve the system of equations by the...

Question 10

Solve using the elimination method.
-x + 3y = 13 
2x + 3y = 8
A)No solution
B)(5, 5)
C)(-4, -5)
D)(-5, 6)

Accepted Answer

The answer of Solve using the elimination method.
-x + 3y...

Question 11

Solve the system of equations by the elimination method.
-x - 2y = 8 
-7x - 3y = -39
A)(6, -1)
B)no solution
C)(5, 0)
D)(-6, 0)

Accepted Answer

To solve the system of equations by the elimination method, we can multiply the first equation by 3 and the second equation by 2 to eliminate the y variable:1st equation: $3(x - 2y) = 3(8)$ => $3x - 6y = 24$2nd equation: $2(-7x - 3y) = 2(-39)$ => $-14x - 6y = -78$Adding these two equations together to eliminate y:$3x - 14x = 24 - 78$$-11x = -54$$x = \frac{-54}{-11} = 6$Substitute $x = 6$ into the first original equation to find y:$6 - 2y = 8$$-2y = 8 - 6$$-2y = 2$$y = -1$Therefore, the solution is $x = 6$, $y = -1$, which corresponds to choice (A)(6, -1).

Question 12

Solve the problem using the elimination method.
-There were 31,000 people at a ball game in Los Angeles. The day's receipts were $180,000. How many people paid $11 for reserved seats and how many paid $4 for general admission?
A)23,000 paid $11 and 8000 paid $4
B)17,000 paid $11 and 14,000 paid $4
C)8000 paid $11 and 23,000 paid $4
D)14,000 paid $11 and 17,000 paid $4

Accepted Answer

The answer of Solve the problem using the elimination method.
-There...

Question 13

Solve the system of equations by the elimination method.
-x + 5y = 25 
2x + 6y = 30
A)(-5, 0)
B)no solution
C)(0, 5)
D)(1, 4)

Accepted Answer

To solve the system of equations by the elimination method, we can multiply the first equation by 2 to align the coefficients of x for elimination:1st equation: $x + 5y = 25$ becomes $2x + 10y = 50$2nd equation: $2x + 6y = 30$Subtracting the second equation from the modified first equation:$(2x + 10y) - (2x + 6y) = 50 - 30$This simplifies to $4y = 20$, and solving for $y$ gives $y = 5$.Substituting $y = 5$ into the first original equation:$x + 5(5) = 25$$x + 25 = 25$$x = 0$Therefore, the solution is $x = 0, y = 5$, which corresponds to choice (C).

Question 14

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°

Accepted Answer

The answer of Solve the problem using the elimination method.
-In...

Question 15

Solve the system of equations by the elimination method.
-$\begin{array} { l } 
\frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 21 \
\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 7
\end{array}$
A) $( - 12,9 )$
B) $( 12,9 )$
C) $( 9 , - 12 )$
D) $( - 12 , - 9 )$

Accepted Answer

To solve the system of equations by the elimination method, first, we need to make the coefficients of either $x$ or $y$ the same in both equations. Let's choose to equalize the coefficients of $x$.The first equation is $\frac{3}{2}x - \frac{1}{3}y = -21$, and the second equation is $\frac{3}{4}x + \frac{2}{9}y = -7$.To equalize the coefficients of $x$, we can multiply the entire second equation by 2, resulting in $\frac{3}{2}x + \frac{4}{9}y = -14$.Now, we have:1. $\frac{3}{2}x - \frac{1}{3}y = -21$2. $\frac{3}{2}x + \frac{4}{9}y = -14$Subtract the second equation from the first to eliminate $x$:$-\frac{1}{3}y - \frac{4}{9}y = -21 + 14$Combining the $y$ terms gives us:$-\frac{3}{9}y - \frac{4}{9}y = -7$$-\frac{7}{9}y = -7$Solving for $y$ gives:$y = -7 \times \frac{-9}{7} = 9$Now, substitute $y = 9$ into one of the original equations to solve for $x$. Using the first equation:$\frac{3}{2}x - \frac{1}{3}(9) = -21$$\frac{3}{2}x - 3 = -21$$\frac{3}{2}x = -18$$x = -18 \times \frac{2}{3} = -12$Therefore, the solution to the system of equations is $x = -12$ and $y = 9$, which corresponds to choice A $(-12, 9)$.

Question 16

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)35°
B)145°
C)105°
D)75°

Accepted Answer

The two angles are supplementary, meaning their sum is 180°. Let x be the smaller angle, then the other angle is 3x + 40. The equation is x + (3x + 40) = 180. Solving for x gives x = 35°, which is the smaller angle.

Question 17

Solve the system of equations by the elimination method.
-2.5x + 0.2y = 10.6 
0.5x - 0.4y = 0.8
A)(4.5, 3)
B)(6.5, 3.2)
C)(4, 3)
D)(1.5, 3.2)

Accepted Answer

To eliminate y, multiply the first equation by 2 and the second by 1, then add them: 5x + 0.4y = 21.2 and 0.5x - 0.4y = 0.8. Adding gives 5.5x = 22, so x = 4. Substitute x = 4 into the first equation to find y = 3.

Question 18

Solve the system of equations by the elimination method.
-0.1x + 0.7y = 1.7 
x - 0.3y = -4.9
A)(-4, 3)
B)(3, -4)
C)(-0.4, 0.3)
D)no solution

Accepted Answer

To solve the system of equations by the elimination method, we first align the equations and then attempt to eliminate one of the variables by adding or subtracting the equations. The given system is:1) $0.1x + 0.7y = 1.7$2) $x - 0.3y = -4.9$First, we can multiply the first equation by 10 to get rid of the decimals, resulting in:$x + 7y = 17$Now, we have:1) $x + 7y = 17$2) $x - 0.3y = -4.9$To eliminate $x$, we can subtract the second equation from the first:$(x + 7y) - (x - 0.3y) = 17 - (-4.9)$$7y + 0.3y = 21.9$$7.3y = 21.9$$y = 3$Substitute $y = 3$ into one of the original equations to find $x$. Using the second equation:$x - 0.3(3) = -4.9$$x - 0.9 = -4.9$$x = -4$Therefore, the solution is $x = -4$, $y = 3$, which corresponds to choice (A) (-4, 3).

Question 19

Solve the problem using the elimination method.
-A salesman sold $300 more than the rest of the sales staff. If the sales total for the day was $1050, how much did the rest of the sales staff sell?
A)$375
B)$675
C)$750
D)$525

Accepted Answer

The salesman sold $300 more than the rest of the sales staff, so the rest of the sales staff sold $1050 - $300 = $750.

Question 20

Solve the system of equations by the elimination method.
--3x - 2y = 4 
12x + 8y = -16
A)(-12, -8)
B)infinitely many solutions
C)(-8, -12)
D)no solution

Accepted Answer

The given system of equations is -3x - 2y = 4 and 12x + 8y = -16. If we multiply the first equation by 4, we get -12x - 8y = 16, which is a multiple of the second equation (12x + 8y = -16) when multiplied by -1. This means the two lines are coincident, and there are infinitely many solutions.

Quiz 8: Systems of Equations

Solve the system of equations by the elimination method. -x + 8y = 8 6x + 9y = 48

Solve the system of equations by the elimination method. - $\begin{array} { l } \frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 18 \\\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 9\end{array}$

Solve the system of equations by the elimination method. --4x + 4y = 6 12x - 12y = 18

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.

Solve the system of equations by the elimination method. -0.8x + 0.3y = 10.7 -0.3x - 0.1y = -3.9

Solve the system of equations by the elimination method. -9x + 7y = 49 -3x - 5y = -35

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 $144 for 5 days and 600 miles. What does Best Rental charge per day and Per mile?

Solve the problem using the elimination method. -There were 380 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $600. How many adults and how many children attended?

Solve the system of equations by the elimination method. --7x + 9y = 28 -3x - 3y = 12

Solve using the elimination method. -x + 3y = 13 2x + 3y = 8

Solve the system of equations by the elimination method. -x - 2y = 8 -7x - 3y = -39

Solve the problem using the elimination method. -There were 31,000 people at a ball game in Los Angeles. The day's receipts were $180,000. How many people paid $11 for reserved seats and how many paid $4 for general admission?

Solve the system of equations by the elimination method. -x + 5y = 25 2x + 6y = 30

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.

Solve the system of equations by the elimination method. - $\begin{array} { l } \frac { 3 } { 2 } x - \frac { 1 } { 3 } y = - 21 \\\frac { 3 } { 4 } x + \frac { 2 } { 9 } y = - 7\end{array}$

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.

Solve the system of equations by the elimination method. -2.5x + 0.2y = 10.6 0.5x - 0.4y = 0.8

Solve the system of equations by the elimination method. -0.1x + 0.7y = 1.7 x - 0.3y = -4.9

Solve the problem using the elimination method. -A salesman sold $300 more than the rest of the sales staff. If the sales total for the day was $1050, how much did the rest of the sales staff sell?

Solve the system of equations by the elimination method. --3x - 2y = 4 12x + 8y = -16