# Exam: 250314RR - Systems of Equations and Inequalities

Exam: 250314RR - Systems of Equations and Inequalities
1. Use the addition method to solve the system below.

A. {(5, 0)}
B. {(5, 0), (–5, 0)}
C. {(0, 5), (0, –5)}
D. {(0, 5)}

2. Graph the inequality x + y < –4.

3. Which operation listed below is not possible for
A. AB
B. 4A
C. A + B
D. A - 2B

4. A system of equations in x, y, and z was converted into the following augmented matrix. What is the
solution to the system?

A. (11,-7,-47)
B. (-1,4,-7)
C. No solution
D. (0,3.6,-5.5)

5. Solve the system below by the method of your choice. Identify systems with no solution and systems with infinitely many solutions using set notation to express their solution sets.
y = 6 - 2x
4x + 2y = 12
A. {(0, 6)}
B. Ø
C. {(5, –4)}
D. {(x, y)|2x + y = 6}

6. Write the partial fraction decomposition of the rational expression below.

7. Which of these properties is true for matrix addition but not matrix multiplication?
A. Some matrices don’t have inverses.
B. There’s an identity.
C. It’s commutative.
D. It’s associative.

8. Graph the inequality x +y < –5.

9. Use the substitution method to solve the system below.

A. {(–2, 5), (–3, 6)}
B. {(3, 0)}
C. {(2, 1), (3, 0)}
D. {(2, 5), (3, 0)}

10. A steel company produces two types of machine dies, part A and part B. The company makes a \$3.00 profit on each part A that it produces and a \$6.00 profit on each part B that it produces. Let x = the number of part A produced in a week and y = the number of part B produced in a week. Write the objective function that describes the total weekly profit.
A. z = 6x + 3y
B. z = 3x + 6y
C. z = 9(x + y)
D. z = 3(x – 6) + 6(y – 3)

11. Which operation was performed on the matrix on the left below to yield the matrix on the right?

12. Classify the system x + y + z = 1, x - y - z = 2.
A. It has a unique solution, (1.5,1.0, -1.5).
B. It has fewer equations than variables, and therefore it has infinitely many solutions.
C. It has fewer equations than variables, but may still have a unique solution.
D. It has fewer equations than variables, and therefore it is inconsistent.

13. Which one of the following ordered pairs is a solution of the system below?

14. Graph the inequality x
15. After computing the determinants required by Cramer's Rule for a system of three equations in three
variables, we obtained the following values. What's the solution to the system?

16. Write the partial fraction decomposition of the rational expression below.

17. Write the partial fraction decomposition of the rational expression below.

18. Which of the following equations comes from the system used to create the augmented matrix ?

A. 4x - 4y = 0
B. 2x - 6y = 0
C. -4x + 4y = 14
D. -8x - 24y = 0

19. Compute the optimal traffic flow along each of the four roads marked x, y, z, and w in the diagram of the city block below.

A. There's one correct answer, which is x = 500, y = 500, z = 100, w = 1900.
B. There's one correct answer, which is x = 400, y = 600, z = 200, w = 900.
C. There are infinitely many correct answers, one of which is x = 400, y = 600, z = 200, w = 900.
D. There's no solution, because the system is dependent.

20. Compute
A. -17
B. -19
C. -16
D. -18