# Solving Problems with Systems of Equations Chapter Exam

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Question 1
1.
Make *x* the subject in the equation: 4*y* - 2*x* = 10.

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Question 2
2.
How would you check values for *x* and *y* after solving linear equations in *x* and *y*?

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Question 3
3.
Substitute *y* = 3*x* - 2 for *y* in 2*y* + 3*x* = 10 and solve for *x*.

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Question 4
4.
If 2*x* - 5*y* = 3 and *x* is equal to 2, what is the value for *y*?

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Question 5
5.
Make *y* the subject in the equation: 4*y* + 2*x* = 6.

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Question 6
6.
Given the following system of equations:

2x + y = 8

3x - 2y = 5

Explain how to solve this system of equations by linear combination.

Which variable will you eliminate?

Which equation will you change by multiplication?

By what number will you multiply?

Will you then add or subtract similar terms?

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Question 7
7.
Solve this system of equation using the linear combination:

x + 2y = -7

3x - 8y = 7

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Question 8
8.
Given the system of equations:

4x - 5y = 23 (Equation C)

3x + 10y = 31 (Equation D)

If Equation C was multiplied by 2 on each side of the equation, which variable would be eliminated?

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Question 9
9.
Which ordered pair is a solution to this system of equations:

2x + y = 2

x - y = 4

#### Question 10 10. In our lesson, what two KEY properties were used to help prove that a solution is the same regardless of how we combine linear equations?

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#### Question 11 11. Which of the following statements are true?

#### Question 12 12. Which of the following is a solution to the system of linear equations shown?

#### Question 13 13. Which of the following are steps in solving a system of linear equations by graphing?

#### Question 14 14. A graph of a system of linear equations is shown along with the system. What is the solution to the system?

#### Question 15 15. Which of the following statements are true.

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Question 16
16.
Which equation represents the first step to solving the following system of equations using the substitution method?

2x - y = 7

x = 2y - 1

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Question 17
17.
Solve the following system of equations:

2x - 3y = 21 and 5x + 4y = 18

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Question 18
18.
Which equation represents the first step to solving the following system of equations using the elimination method?

2x - 2y = 5 and -4x + 5y = 11

#### Question 19 19. If trying to figure out how many $5 burritos and $3 tacos to buy, which equation represents the situation where you have $100 to spend?

#### Question 20 20. A car company has $44,000 to spend on robots to put paint on new cars. There are 2 types of robots, some that cost $3,000 and some that cost $2,000. If the company is sure that it wants to spend all of its money on 16 new robots, how many of each should it purchase?

### Page 5

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Question 21
21.
Which of the following points is a solution to the equation *f*(*x*) = 3*x* + 2?

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Question 22
22.
If the intersection point of the graphs of *f*(*x*) and *g*(*x*) is (-3,-10), which of the following statements is NOT true?

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Question 23
23.
The graphs of *f*(*x*) = 4*x* - 5 and *g*(*x*) = -*x* are shown along with their intersection point (1,-1). Based on this, what value of *x* will make *f*(*x*) = *g*(*x*)?

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Question 24
24.
If (3,1) is a solution to both *f*(*x*) = *x* - 2 and *g*(*x*) = -2*x* + 7, then which of the following statements is true?

#### Question 25 25. Which of the following statements is NOT true?

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#### Question 26 26. Which graph does NOT represent a system of equations?

#### Question 27 27. Look at the graph. What is the solution to the system of equations?

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Question 28
28.
Find the solution, given the system of equations below.

y = 3x - 5

y = -2x + 10

#### Question 29 29. What is the solution to the system of equations shown in the graph below?

#### Question 30 30. Two companies charge different amounts for renting a car. Company A charges a lot up front, but not much per day. Company B lets you have the car for cheap, but then makes you pay a lot every day you have the car. If we have two equations that represent these two companies, and we solve this system of equations, what will we find?

#### Solving Problems with Systems of Equations Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!