# OAE Mathematics: Systems of Equations Chapter Exam

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### Page 1

#### Question 1 1. Use Cramer's rule to find the z solution to this linear system.

#### Question 2 2. If two equations produce a false statement in a linear system in three variables, how many solutions does this system have?

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

#### Question 4 4. 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 5
5.
Solve this system.

4x + y = 12

x + y = 6

### Page 2

####
Question 6
6.
Solve.

x - y = 6

x + y = 10

#### Question 7 7. To find D sub y, which column of the coefficient matrix would you replace with the constant numbers?

#### Question 8 8. Which equation(s) need to be rewritten in this linear system before we can write it in augmented matrix form?

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

#### Question 10 10. How many more equations are needed to complete this linear system with three variables?

### Page 3

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

#### Question 12 12. How many determinants do you need to find in order to solve a linear system in three variables using Cramer's rule?

#### Question 13 13. What is the determinant of the coefficient matrix for this linear system?

#### Question 14 14. If a linear system has three variables, how many equations are needed to complete the system?

####
Question 15
15.
Solve this system.

x + y = 6

y = 2x

### Page 4

#### Question 16 16. Solve this system.

#### Question 17 17. What are the most common letters we will see for our variables?

#### Question 18 18. Which method can be used to solve any system of linear equations in two variables?

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

#### Question 20 20. Write in augmented matrix form.

### Page 5

#### Question 21 21. How many solutions does this system have?

####
Question 22
22.
Find the y solution of this system using Cramer's rule.

2x + 2y = 10

3x - 2y = 0

####
Question 23
23.
What is the determinant of the coefficient matrix of this linear system?

2x + 2y = 10

3x - 2y = 0

#### Question 24 24. Which of the following is an equation included in this matrix?

#### Question 25 25. 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 6

####
Question 26
26.
Find the x solution of this system using Cramer's rule.

2x + 2y = 10

3x - 2y = 0

#### Question 27 27. Which column do you replace in the coefficient matrix if you want to solve for the y solution?

####
Question 28
28.
In this system of equations, which numbers are your constant numbers?

x + 3y - 2z = 18

2x - y - z = -7

4x - 2y + z = -8

#### Question 29 29. Which of the following will work?

#### Question 30 30. What is the first step in the substitution method?

#### OAE Mathematics: 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!