Exam: 250314RR – Systems of Equations and Inequalities

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Exam: 250314rr – systems of equations and inequalities

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1. Compute

A. -17

B. -16

C. -19

D. -18

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

A. 2x – 6y = 0

B. -8x – 24y = 0

C. -4x + 4y = 14

D. 4x – 4y = 0

3. Graph the inequality –2x – 3y = 6.

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

A.

B.

C.

D.

5. 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?

6. Which operation listed below is not possible for

A. AB

B. 4A

C. A + B

D. A – 2B

7. Graph the solution set of the system of inequalities below.

y < -x + 10

y > 3x – 3

8. Solve the system below by the substitution method.

A. {(5, 11), (6, 0)}

B. {(–5, 11), (–6, 12)}

C. {(6, 0)}

D. {(5, 1), (6, 0)}

9. 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 is inconsistent.

C. It has fewer equations than variables, and therefore it has infinitely many solutions.

D. It has fewer equations than variables, but may still have a unique solution.

10. Given the values below, solve for X in AX = B.

11. If , then which of these statements is true?

12. Which matrix is the inverse of ?

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

14. Use the substitution method to solve the system of equations below.

5x + 2y = -68

x = 3y

A. {(–12, 4)}

B. {(–11, –4)}

C. {(–4, –12)}

D. {(–12, –4)}

15. A steel company produces two types of machine dies, part A and part B, and is bound by the following constraints:

• Part A requires 1 hour of casting time and 10 hours of firing time.

• Part B requires 4 hours of casting time and 3 hours of firing time.

• The maximum numbers of hours per week available for casting and firing are 100 and 70, respectively.

• The cost to the company is $0.75 per part A and $3.00 per part B. Total weekly costs can’t exceed $45.00.

Let x = the number of part A produced in a week and y = the number of part B produced in a week. Write a system of three inequalities that describes these constraints.

16. Graph the inequality x +y < –5.

17. Use the addition method to solve the system below.

A. {(0, 5)}

B. {(5, 0)}

C. {(5, 0), (–5, 0)}

D. {(0, 5), (0, –5)}

18. Use the substitution method to solve the system of equations below.

x = – 4y

A. {(36, 9)}

B. {(36, -9)}

C. {(-9, 36)}

D. {(37, -9)}

19. Use the addition method to solve the system below.

x – 2y = -14

2x – 3y = -22

A. {(-3, 7)}

B. {(2, 7)}

C. Ø

D. {(-2, 6)}

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

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