AnswersAG Q3 Math 8 25-26 JTurnerMultiplying One Equation to Solve Systems

Multiplying One Equation to Solve Systems — Unit test Answers

15 verified answers
1
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Thomas was selling tickets to his school play. The tickets cost $5.00 for adults and $2.00 for children. He sold 200 tickets and collected $610. Which system represents the number of adult and child tickets that Thomas sold?

A
x + y = 200. 5 x + 2 y = 610.
Option A
B
x + y = 610. 5 x + 2 y = 200.
Option B
C
x + y = 200. x + 2 y = 610.
Option C
D
x + y = 200. 5 x + y = 610.
Option D
2
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Which system of equations shows a solution of (0.5, –1)?

A
On a coordinate plane, 2 lines intersect at (0.5, negative 1).
Option A
B
On a coordinate plane, 2 lines intersect at (negative 0.5, negative 1).
Option B
C
On a coordinate plane, 2 lines intersect at (negative 0.5, 1).
Option C
D
On a coordinate plane, 2 lines intersect at (0.5, 1).
Option D
3

Arnoldo needs to write this system in slope-intercept form. Which shows how he could do that?

Question illustration
A
y = negative three-halves x + 3
Option A
B
y = three-halves x minus 3
Option B
C
y = negative three-halves x minus 3
Option C
D
y = three-halves x minus 3
Option D
4

In the system of equations below, which variable would it be easiest to solve for?

Question illustration
A
The easiest to solve for is x in the first equation.
B
The easiest to solve for is y in the first equation.
C
The easiest to solve for is x in the second equation.
D
The easiest to solve for is y in the second equation.
5

What is the solution to the system of equations below? and

Question illustration
A
(21, 2)
B
(21, –10)
C
(–21, 16)
D
(–21, –26)
6

Which graph shows the system of equations and ?

Question illustration
A
On a coordinate plane, a line goes through (0, negative 1) and (3, 1) and another line goes through (0, 3) and (1, negative 1).
Option A
B
On a coordinate plane, a line goes through (0, 3) and (1, negative 1) and another line goes through (0, negative 3) and (3, negative 1).
Option B
C
On a coordinate plane, a line goes through (0, 3) and (negative 1, negative 1) and another line goes through (0, negative 3) and (3, negative 1).
Option C
D
On a coordinate plane, a line goes through (0, 3) and (negative 1, negative 1) and another line goes through (0, negative 1) and (3, 1).
Option D
7

Sophia’s math test is worth 130 points and has 40 problems. Each problem is worth either 4 points or 3 points. How many of each question type were on the test?

A
The test had 30 4-point questions and 10 3-point questions.
B
The test had 10 4-point questions and 30 3-point questions.
C
The test had 28 4-point questions and 12 3-point questions.
D
The test had 25 4-point questions and 10 3-point questions.
8

To solve the system of linear equations and by using the linear combination method, Amos decided that he should first multiply the second equation by –5 and then add the two equations together to eliminate the y-terms. His calculations are as shown. Amos’s solution is (2, –14). What did he do wrong?

Question illustration
A
He multiplied the equation by –5 incorrectly.
Option A
B
He added the equations and incorrectly.
Option B
C
He substituted 2 into the equation incorrectly.
Option C
D
He solved the equation for y incorrectly.
Option D
9

What system of equations is shown on the graph below?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
10

What is the solution to the system of equations below? and

Question illustration
A
(3, 9)
B
(8, 12)
C
(12, 8)
D
(9, 3)
11

Which statements about this system of equations are true? Check all that apply

Question illustration
A
The x-variable will be eliminated when adding the system of equations.
B
The y-variable will be eliminated when adding the system of equations.
C
The sum of the system of equations is .
Option C
D
x = 17
Option D
E
y = negative 3
Option E
F
There are infinitely many solutions to the system of equations.
12

Malia did push-ups and pull-ups in her physical education class. She did 24 push-ups and pull-ups combined, with each push-up taking her 2 seconds and each pull-up taking her 4 seconds. If she spent a total of 68 seconds doing the push-ups and pull-ups, how many pull-ups did she do?

A
2
B
4
C
10
D
14
13

The equations , , , and are shown on the graph below. Which system of equations has a solution of approximately (–0.3, 1.4)?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
14

Consider this system of equations. Which equation represents the first equation written in slope-intercept form?

Question illustration
A
y = five-halves x minus 5
Option A
B
y = five-halves x + 10
Option B
C
y = negative five-halves x + 10
Option C
D
y = negative 5 x minus 5
Option D
15

The equations in this sytem were added to solve for x. What is the value of x?

Question illustration
A
x = negative 2
Option A
B
x = negative one-half
Option B
C
x = one-half
Option C
D
x = 2
Option D

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