AnswersAG Q3 Math 8 25-26 JTurnerUnit Test

Unit Test — Unit test Answers

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A number is equal to the sum of half a second number and 3. The first number is also equal to the sum of one-quarter of the second number and 5. The situation can be represented by using the graph below, where x represents the second number. Which equations represent the situation?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
2
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What is the solution to the system of equations below?

Question illustration
A
(Negative 7, 24)
Option A
B
(3, 4)
Option B
C
(4, 3)
Option C
D
(24, Negative 7)
Option D
3

A clothing company sells slacks that are either blue or gray and pleated or non-pleated. Last month, the company sold 5 times as many pairs of blue pleated slacks as gray pleated slacks, and it sold twice as many pairs of gray non-pleated slacks as blue non-pleated slacks. If it sold 333 pairs of blue slacks and 225 pairs of gray slacks, how many pairs of blue non-pleated slacks did it sell?

A
49
B
88
C
176
D
245
4

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

Question illustration
A
(2, –22)
B
(2, 48)
C
(–2, 2)
D
(–2, –20)
5

The system of equations and is shown on the graph below. What is a reasonable estimate for the solution?

Question illustration
A
(1 and three-fourths, 2 and one-half)
Option A
B
(2 and one-half, 1 and three-fourths)
Option B
C
(1 and one-third, 2 and one-half)
Option C
D
(2 and one-half, 1 and one-third)
Option D
6

A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number. Which equations can be used to model the situation? Check all that apply.

A
x = one-half y minus 3
Option A
B
2 x minus y = negative 6
Option B
C
2 x minus y = negative 3
Option C
D
x = one-half (y minus 3)
Option D
E
y = 10 (x minus 1)
Option E
7

Two linear equations are represented by using the tables below.The data points for equation A are graphed on the coordinate plane below and are connected by using a straight line.What is the solution to the system of equations?

Question illustration
A
(–2, –8)
B
(–1, –5)
C
(0, –2)
D
(2, 4)
8

Mr. Berger assigned the following system of equations to be solved for homework. Which is the x-coordinate of the correct solution?

Question illustration
A
x = negative 3
Option A
B
x = negative one-fifth
Option B
C
x = StartFraction 9 Over 7 EndFraction
Option C
D
x = 2
Option D
9

The system of equations and y = –2x + 3 is shown on the graph below. According to the graph, what is the solution to this system of equations?

Question illustration
A
(5, –7)
B
(–7, 5)
C
(5, 7)
D
(7, 5)
10

A company has a $150 budget to provide lunch for its 20 employees. The options are to provide either roast beef sandwiches, which cost $5 apiece, or tuna sandwiches, which also cost $5 apiece. The company also wants to use the entire budget. Suppose r represents the number of roast beef sandwiches it provides and t represents the number of tuna sandwiches. Which statement is correct?

A
The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations and .
Option A
B
The company can provide lunch for all 20 employees and use the entire budget because there is a solution to the system of equations and .
Option B
C
The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations and .
Option C
D
The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations and .
Option D
11

In this system of equations, 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.
12

A larger number is double the sum of 3 and a smaller number. The larger number is 2 less than 3 times the smaller number. If y represents the larger number and x represents the smaller number, which equations model the situation? Check all that apply.

A
y = 3 x minus 2
Option A
B
3 x minus y = 2
Option B
C
3 x minus y = negative 2
Option C
D
y = 2 minus 3 x
Option D
E
y = 2 (x + 3)
Option E
13

What is the solution to this system of equations?

Question illustration
A
(4, negative one-fourth)
Option A
B
(4, negative StartFraction 9 Over 16 EndFraction)
Option B
C
no solution
D
infinitely many solutions
14

The linear combination method gives a solution of (–4, 2) for which of these systems of linear equations?

A
3 x + 13 y = 14. 6 x + 11 y = negative 2.
Option A
B
4 x + 5 y = 12. 8 x + 3 y = negative 4.
Option B
C
5 x + 4 y = 12. 7 x + 8 y = 12.
Option C
D
10 x + 3 y = 8. 17 x + 6 y = 10.
Option D
15

A number is equal to 3 times a smaller number. Also, the sum of the smaller number and 4 is the larger number. The situation is graphed on the coordinate plane below, where x represents the smaller number and y represents the larger number. Which two equations represent the situation?

Question illustration
A
and
Option A
B
and
Option B
C
and
Option C
D
and
Option D
16

Use the linear combination method to solve this system of equations. What is the value of x?

Question illustration
A
Negative 1
Option A
B
0
C
1
D
4.8
Option D
17

Which system of equations below has exactly one solution?

A
y = –8x – 6 and y = –8x + 6
B
y = –8x – 6 and y = –4x – 3
Option B
C
y = –8x – 6 and y = 8x – 6
D
y = –8x – 6 and –y = 8x + 6
18

Michiko claims that to solve the system of linear equations and , instead of multiplying the second equation by –2 and then adding the equations, she could multiply the second equation by 2 and then subtract the second equation from the first equation. Which statement is correct?

Question illustration
A
Michiko is right for this system of linear equations, but her method will not work for other systems of linear equations.
B
Michiko is right for this system of linear equations, and her method will also work for other systems of linear equations.
C
Michiko is wrong because her method will give the opposite of the correct value for x for any system of linear equations.
D
Michiko is wrong because her method will give the opposite of the correct value for y for any system of linear equations.
19

The system of equations y = 2x + 5 and y = –3x – 15 is shown on the graph below. According to the graph, what is the solution to this system of equations?

Question illustration
A
(–4, –3)
B
(–3, –4)
C
(–5, 5)
D
(5, –5)
20

Which equation results from adding the equations in this system?

Question illustration
A
5 x = negative 10
Option A
B
5 x = 26
Option B
C
Negative 5 x = 26
Option C
D
Negative 5 x = negative 10
Option D

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