# NES Math: Systems of Equations Chapter Exam

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### Page 1

#### Question 1 1. What is the first step in the substitution method?

#### Question 2 2. How many determinants do you need to find in order to solve a linear system in three variables using Cramer's rule?

#### Question 3 3. Which of the following will work?

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Question 4
4.
Find the y solution of this system using Cramer's rule.

2x + 2y = 10

3x - 2y = 0

#### Question 5 5. How many solutions does this system have?

### Page 2

#### Question 6 6. Write in augmented matrix form.

#### Question 7 7. Which of the following is an equation included in this matrix?

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Question 8
8.
What is the determinant of the coefficient matrix of this linear system?

2x + 2y = 10

3x - 2y = 0

#### Question 9 9. For a linear system with two variables, how many determinants do we need to find to find the complete solution using Cramer's rule?

#### Question 10 10. Which column do you replace in the coefficient matrix if you want to solve for the y solution?

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#### Question 11 11. What are the most common letters we will see for our variables?

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Question 12
12.
Find the x solution of this system using Cramer's rule.

2x + 2y = 10

3x - 2y = 0

#### Question 13 13. Which method can be used to solve any system of linear equations in two variables?

#### Question 14 14. To find D sub y, which column of the coefficient matrix would you replace with the constant numbers?

#### Question 15 15. 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:

### Page 4

#### Question 16 16. What is the determinant of the coefficient matrix for this linear system?

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Question 17
17.
In this system of equations, which numbers are your constant numbers?

x + 3y - 2z = 18

2x - y - z = -7

4x - 2y + z = -8

#### Question 18 18. How many solutions does this system have?

#### Question 19 19. What is the complete list of equations included in this augmented matrix?

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Question 20
20.
Solve.

x - y = 6

x + y = 10

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#### Question 21 21. Use Cramer's rule to find the z solution to this linear system.

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Question 22
22.
Solve this system.

x + y = 6

y = 2x

#### Question 23 23. How many more equations are needed to complete this linear system with three variables?

#### Question 24 24. Solve this system.

#### Question 25 25. Rewrite the 3rd equation in proper form so that we can turn it into augmented matrix form.

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Question 26
26.
Solve this system.

4x + y = 12

x + y = 6

#### Question 27 27. If two equations produce a false statement in a linear system in three variables, how many solutions does this system have?

#### Question 28 28. If a linear system has three variables, how many equations are needed to complete the system?

#### Question 29 29. Which equation(s) need to be rewritten in this linear system before we can write it in augmented matrix form?

#### Question 30 30. How many variables does a linear system in three variables have?

#### NES Math: 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!