# GACE Math: Systems of Equations Chapter Exam

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#### Question 1 1. If two equations produce a false statement in a linear system in three variables, how many solutions does this system have?

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Question 2
2.
In this system of equations, which numbers are your constant numbers?

x + 3y - 2z = 18

2x - y - z = -7

4x - 2y + z = -8

#### Question 3 3. Which column do you replace in the coefficient matrix if you want to solve for the y solution?

#### Question 4 4. Solve this system.

#### Question 5 5. 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:

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#### Question 6 6. Use Cramer's rule to find the z solution to this linear system.

#### Question 7 7. Which method can be used to solve any system of linear equations in two variables?

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Question 8
8.
Find the x solution of this system using Cramer's rule.

2x + 2y = 10

3x - 2y = 0

#### Question 9 9. What is the complete list of equations included in this augmented matrix?

#### Question 10 10. What is the first step in the substitution method?

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#### Question 11 11. How many solutions does this system have?

#### Question 12 12. If a linear system has three variables, how many equations are needed to complete the system?

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Question 13
13.
Find the y solution of this system using Cramer's rule.

2x + 2y = 10

3x - 2y = 0

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Question 14
14.
Solve this system.

x + y = 6

y = 2x

#### Question 15 15. How many determinants do you need to find in order to solve a linear system in three variables using Cramer's rule?

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Question 16
16.
Solve.

x - y = 6

x + y = 10

#### Question 17 17. Which of the following is an equation included in this matrix?

#### Question 18 18. To find D sub y, which column of the coefficient matrix would you replace with the constant numbers?

#### Question 19 19. How many variables does a linear system in three variables have?

#### Question 20 20. Which equation(s) need to be rewritten in this linear system before we can write it in augmented matrix form?

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#### Question 21 21. Which of the following will work?

#### Question 22 22. What is the determinant of the coefficient matrix for this linear system?

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Question 23
23.
Solve this system.

4x + y = 12

x + y = 6

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Question 24
24.
What is the determinant of the coefficient matrix of this linear system?

2x + 2y = 10

3x - 2y = 0

#### Question 25 25. What are the most common letters we will see for our variables?

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#### Question 26 26. Write in augmented matrix form.

#### Question 27 27. How many more equations are needed to complete this linear system with three variables?

#### Question 28 28. 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 29 29. Rewrite the 3rd equation in proper form so that we can turn it into augmented matrix form.

#### Question 30 30. How many solutions does this system have?

#### GACE 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!