# Graph the inequality - Expert Answers

1. Graph the inequality x +y < –5.

2. Compute

A. -19

B. -18

C. -17

D. -16

3. 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 no solution, because the system is dependent.

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 one correct answer, which is x = 500, y = 500, z = 100, w = 1900.

4. Solve the system of equations below.

x + y = 6

3 x - 4y - 4z = -9

x- z = 3

A. {(–2, 1, 5)}

B. {(1, –2, 5)}

C. {(–2, 5, 1)}

D. {(1, 5, –2)}

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

x + y = 1

x- y = 9

A. (5, 4)

B. (–5, –4)

C. (5, –4)

D. (–5, 4)

6. 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.

7. Graph the inequality –2x – 3y = 6.

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

9. Solve the system below by the addition method.

A. {(0, 3), (0, –3)}

B. {(3, 0), (–3, 0)}

C. {(0, 3)}

D. {(3, 0)}

10. Graph the inequality x

11. Which of the following augmented matrices represents a dependent system?

12. Write the partial fraction decomposition of the rational

expression below.

13. Which of the following is true about the identity matrix In?

A. Any matrix A has the same order as every I

B. Any matrix A can be multiplied by some I

C. Any matrix A can be multiplied by some I

D. Every I

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

-4x - 3y = -117

x = - 4y

A. {(36, 9)}

B. {(36, -9)}

C. {(-9, 36)}

D. {(37, -9)}

15. Solve the system below by the method of your choice.

A. {(0, 0), (8, –512)}

B. {(–1, 1), (–8, 512)}

C. {(0, 0), (–8, 64)}

D. {(0, 0), (–8, 512)}

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

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

A. {(2, 1), (3, 0)}

B. {(3, 0)}

C. {(–2, 5), (–3, 6)}

D. {(2, 5), (3, 0)}

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

x + 3y = 8

-2x + 2y = 16

A. {(4, 5)}

B. {(–4, 4)}

C. 0

D. {(–5, 5)}

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

A. -4x + 4y = 14

B. 2x - 6y = 0

C. 4x - 4y = 0

D. -8x - 24y = 0

20. 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 = 3(x – 6) + 6(y – 3)

B. z = 3x + 6y

C. z = 9(x + y)

D. z = 6x + 3y

2. Compute

A. -19

B. -18

C. -17

D. -16

3. 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 no solution, because the system is dependent.

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 one correct answer, which is x = 500, y = 500, z = 100, w = 1900.

4. Solve the system of equations below.

x + y = 6

3 x - 4y - 4z = -9

x- z = 3

A. {(–2, 1, 5)}

B. {(1, –2, 5)}

C. {(–2, 5, 1)}

D. {(1, 5, –2)}

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

x + y = 1

x- y = 9

A. (5, 4)

B. (–5, –4)

C. (5, –4)

D. (–5, 4)

6. 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.

7. Graph the inequality –2x – 3y = 6.

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

9. Solve the system below by the addition method.

A. {(0, 3), (0, –3)}

B. {(3, 0), (–3, 0)}

C. {(0, 3)}

D. {(3, 0)}

10. Graph the inequality x

11. Which of the following augmented matrices represents a dependent system?

12. Write the partial fraction decomposition of the rational

expression below.

13. Which of the following is true about the identity matrix In?

A. Any matrix A has the same order as every I

B. Any matrix A can be multiplied by some I

C. Any matrix A can be multiplied by some I

D. Every I

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

-4x - 3y = -117

x = - 4y

A. {(36, 9)}

B. {(36, -9)}

C. {(-9, 36)}

D. {(37, -9)}

15. Solve the system below by the method of your choice.

A. {(0, 0), (8, –512)}

B. {(–1, 1), (–8, 512)}

C. {(0, 0), (–8, 64)}

D. {(0, 0), (–8, 512)}

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

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

A. {(2, 1), (3, 0)}

B. {(3, 0)}

C. {(–2, 5), (–3, 6)}

D. {(2, 5), (3, 0)}

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

x + 3y = 8

-2x + 2y = 16

A. {(4, 5)}

B. {(–4, 4)}

C. 0

D. {(–5, 5)}

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

A. -4x + 4y = 14

B. 2x - 6y = 0

C. 4x - 4y = 0

D. -8x - 24y = 0

20. 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 = 3(x – 6) + 6(y – 3)

B. z = 3x + 6y

C. z = 9(x + y)

D. z = 6x + 3y

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