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Solving Problems with Systems of Equations Chapter Exam

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!

Page 1

Question 1 1. Which of the following statements is NOT true?

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

Question 3 3. The graphs of f(x) = 4x - 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)?

Question 4 4. If (3,1) is a solution to both f(x) = x - 2 and g(x) = -2x + 7, then which of the following statements is true?

Question 5 5. If the intersection point of the graphs of f(x) and g(x) is (-3,-10), which of the following statements is NOT true?

Page 2

Question 6 6. A graph of a system of linear equations is shown along with the system. What is the solution to the system?

Question 7 7. Which of the following statements are true.

Question 8 8. Which of the following statements are true?

Question 9 9. Which of the following are steps in solving a system of linear equations by graphing?

Question 10 10. Which of the following is a solution to the system of linear equations shown?

Page 3

Question 11 11. Substitute y = 3x - 2 for y in 2y + 3x = 10 and solve for x.

Question 12 12. If 2x - 5y = 3 and x is equal to 2, what is the value for y?

Question 13 13. Make y the subject in the equation: 4y + 2x = 6.

Question 14 14. How would you check values for x and y after solving linear equations in x and y?

Question 15 15. Make x the subject in the equation: 4y - 2x = 10.

Page 4

Question 16 16.

Solve this system of equation using the linear combination:

x + 2y = -7

3x - 8y = 7

Question 17 17.

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?

Question 18 18.

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?

Question 19 19.

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

2x + y = 2

x - y = 4

Question 20 20. 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?

Page 5

Question 21 21. Which graph does NOT represent a system of equations?

Question 22 22. Based on this graph, what is the solution to the system of equations?

Question 23 23. Consider the following two car rental companies. Cars R Us charges $100 up front, plus 10 cents per mile. Thrifty Car Rentals charges 25 cents per mile with no upfront fee. If TC represent the total cost for the car, and n represents the number of miles, which of the following systems of equations best represents this situation?

Question 24 24.

Solve the system of equations below:

y = 3x - 5

y = -2x + 10

Question 25 25. Which of the following is a solution to the system of equations shown in the graph below?

Page 6

Question 26 26.

Solve the following system of equations:

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

Question 27 27.

Which of the following represents a valid first step to solving this system of equations using the substitution method?

2x - y = 7

x = 2y - 1

Question 28 28.

Which equation represents a valid first step to solving the following system of equations using the elimination method if our next step is to add the equations together to eliminate the x variable?

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

Question 29 29. 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?

Question 30 30. When trying to figure out how many $5 burritos and $3 tacos to buy, which equation represents the situation where you have $100 to spend?

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!

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