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Systems of Equations & Inequalities 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.

Solve this system.

4x + y = 12

x + y = 6

Question 2 2.

Solve.

x - y = 6

x + y = 10

Question 3 3. What is the first step in the substitution method?

Question 4 4. Which of the following statements is NOT true?

Question 5 5. Which of the following points is a solution to the equation f(x) = 3x + 2?

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Question 6 6. 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 7 7.

Solve.

y = x

y = 2x + 4

Question 8 8. What is the solution?

Question 9 9. How many equations can you have in a system of equations?

Question 10 10. The following graph shows a system of non-linear equations with a quadratic equation and a linear equation. How many solutions does the system of equations have?

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Question 11 11. Consider the following non-linear system of equations, which includes a linear and a quadratic equation. What would you do first to solve the system algebraically using substitution?

Question 12 12. When solving the following system of equations algebraically, what would be the resulting equation? Hint: you already have the solution for y.

Question 13 13.

Solve the system of equations below:

y = 3x - 5

y = -2x + 10

Question 14 14. Which of the following is a solution to the system of equations shown in the graph below?

Question 15 15. Which graph does NOT represent a system of equations?

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Question 16 16.

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 17 17. 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 18 18.

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 19 19. How many equations will be in your system of equations if you have the variables a, b, c, d, and e in your problem?

Question 20 20.

Solve for x.

x + y + z = 4

4x - y - z = 1

x + z = 2

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Question 21 21.

Solve for y.

x + y + z = 4

4x - y - z = 1

x + z = 2

Question 22 22. What type of lines should be used when graphing inequalities that have >= or <= to signs?

Question 23 23. On the graph, how do you determine which side of the line represents the solution set?

Question 24 24. If the shaded areas on the graph do not all overlap, the solution set is _____.

Question 25 25. Which method can be used to solve any system of linear equations in two variables?

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Question 26 26. If the intersection point of the graphs of f(x) and g(x) is (-3,-10), which of the following statements is NOT true?

Question 27 27. What is the solution?

Question 28 28. The following graph shows the graph of a system of non-linear equations with a quadratic equation and a linear equation. How many solutions does the system have?

Question 29 29. 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 30 30.

Solve the following system of equations:

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

Systems of Equations & Inequalities 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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