6th-8th Grade Algebra: Systems of Linear 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. How many solutions does this system have?

Question 2 2.

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 3 3. Solve this system.

Question 4 4. What are the most common letters we will see for our variables?

Question 5 5. 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?

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Question 6 6.

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 7 7. If a linear system has three variables, how many equations are needed to complete the system?

Question 8 8. Based on this graph, what is the solution to the system of equations?

Question 9 9. How many solutions does this system have?

Question 10 10. 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?

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Question 11 11. How many variables does a linear system in three variables have?

Question 12 12. Which of the following will work?

Question 13 13. If two equations produce a false statement in a linear system in three variables, how many solutions does this system have?

Question 14 14. What is the first step in the substitution method?

Question 15 15. 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?

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Question 16 16.

Solve this system.

4x + y = 12

x + y = 6

Question 17 17. Which of the following is a solution to the system of equations shown in the graph below?

Question 18 18.

Solve.

x - y = 6

x + y = 10

Question 19 19.

Solve this system.

x + y = 6

y = 2x

Question 20 20. How many more equations are needed to complete this linear system with three variables?

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Question 21 21.

Solve the following system of equations:

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

Question 22 22. Which graph does NOT represent a system of equations?

Question 23 23.

Solve the system of equations below:

y = 3x - 5

y = -2x + 10

Question 24 24. If you don't see a variable listed in a linear system in three variables, you should note that the variable has a coefficient of:

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

6th-8th Grade Algebra: Systems of Linear 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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