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# NMTA Math: Systems of Equations Chapter Exam

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### Page 1

#### Question 1 1. Rewrite the 3rd equation in proper form so that we can turn it into augmented matrix form.

#### Question 2 2. Solve this system.

#### Question 3 3. If two equations produce a false statement in a linear system in three variables, how many solutions does this system have?

#### Question 4 4. 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 5 5. How many more equations are needed to complete this linear system with three variables?

### Page 2

#### Question 6 6. How many determinants do you need to find in order to solve a linear system in three variables using Cramer's rule?

####
Question 7
7.
What is the determinant of the coefficient matrix of this linear system?

2x + 2y = 10

3x - 2y = 0

#### Question 8 8. How many solutions does this system have?

####
Question 9
9.
Solve.

x - y = 6

x + y = 10

#### Question 10 10. When using a matrix to solve a system of three variables in three equations, you replace the _____ of the coefficient matrix to solve for the y solution.

### Page 3

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

#### Question 12 12. What is the first step in the substitution method?

####
Question 13
13.
In this system of equations, which numbers are your constant numbers?

x + 3y - 2z = 18

2x - y - z = -7

4x - 2y + z = -8

#### Question 14 14. Which of the following will work?

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

x + y = 6

y = 2x

### Page 4

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

#### Question 17 17. To find D sub y, which column of the coefficient matrix would you replace with the constant numbers?

####
Question 18
18.
Solve this system.

4x + y = 12

x + y = 6

#### Question 19 19. Write in augmented matrix form.

#### Question 20 20. What is the complete list of equations included in this augmented matrix?

### Page 5

#### Question 21 21. Which method can be used to solve any system of linear equations in two variables?

#### Question 22 22. If a linear system has three variables, how many equations are needed to complete the system?

#### Question 23 23. 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 24 24. Use Cramer's rule to find the z solution to this linear system.

####
Question 25
25.
Find the x solution of this system using Cramer's rule.

2x + 2y = 10

3x - 2y = 0

### Page 6

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

2x + 2y = 10

3x - 2y = 0

#### Question 27 27. Which equation(s) need to be rewritten in this linear system before we can write it in augmented matrix form?

#### Question 28 28. Which of the following is an equation included in this matrix?

#### Question 29 29. How many solutions does this system have?

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

#### NMTA 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!