# Exam: 050291RR - Systems of Equations; Inequalities

Exam: 050291RR - Systems of Equations; Inequalities

1. The matrix below is the augmented matrix of a system of three equations in the variables x and y. Solve

for x and y.

A. One solution,

B. One solution (0, 9)

C. No solution

D. Infinitely many solutions

2. Graph the following solution set:

x = y

2

y = x

3. Solve the inequality –2 (3 + x) < 4x + 4 < 8x. Give the result in set notation and graph it.

4. Solve the inequality |2x - 4| < 10. Write the solution in interval notation and graph it.

5. Graph the inequality 3x = –4y - 4.

6. Solve the inequality 4 < –z - 4 < 11. Give the result in set notation and graph it.

7. Which of the following phrases correctly describes the graph of the system of equations

and y = 2 - x?

A. The graph is of two parallel lines that do not intersect.

B. The graph is of two lines that coincide.

C. The graph is of two lines that intersect at a single point.

D. The graph is of a line and a parabola, which intersect at two points.

8. Are the two equations –6 + y = 2x and 2y - 4x = 12 dependent?

A. No, because the equations are not written the same.

B. No, because they are not parallel.

C. Yes, because they have the same graph.

D. Yes, because both are the equations of straight lines.

9. Solve the equation |6x + 3| = 15

A. x = 2

B. x = 4

C. x = –3

D. x = –3 or x = 2

10. Choose the correct ways to fill in the blanks in the following sentence.

To solve a system of equations using the matrix method, use __________ to transform the augmented

matrix into one with __________, then proceed to back-substitute.

A. the coefficient matrix, an inverse

B. the coefficient matrix, Gaussian elimination

C. multiplication and addition, zeros in its final column

D. elementary row operations, zeros below the diagonal

11. Solve the equation |x| = 7.

A. x = 7 or x = –7

B. x = 7

C. x = –7

D. Undefined

12. Solve the system of equations x + y + z = 9, –x + y + z = 1, and x - y - z = 5.

A. There is not enough information to solve the problem.

B. There is one solution, x = 4, y = 2, and z = 3.

C. There are infinitely many solutions.

D. There is no solution.

13. Graph the solution set of

x + 2y = 3

x + 2y = 4

14. Solve the inequality |5x + 10| = 15. Write the solution in interval notation and graph it.

15. Consider two ships, one on a course described by the equation 0.6x + 0.3y = 2.1 and the other on a

course described by the equation –0.3x + 0.1y = –1.8. Which of the following sentences best describes the

possibility of a collision?

A. There is a possibility of a collision at the point (5, –3) but a collision is not a certainty.

B. There is a possibility of a collision at the point (0, 7) but a collision is not a certainty.

C. There is no possibility for a collision.

D. There will certainty be a collision at the point (6, 0).

16. Graph the following solution set:

x + y = 4

x = 0

y = 0

A.

B.

C.

D.

17. Find the equation of the boundary line in the graph below. Then give the inequality represented by the

shaded area.

A.

B.

C.

D.

18. Graph the following solution set:

y = x - 1

y = 2x

A.

B.

C.

D.

19. Solve the inequality . Give the result in set notation and graph it.

A.

B.

C.

D.

20. Find the value of the expression –|–18|.

A. 18

B. –18

C. 0

D. Undefined

21. What is the formula for the determinant of a 3 x 3 matrix ?

22. Graph the inequality y < 3x + 1.

23. Solve the system of equations x - 4y = –8 and –3x + 12y = 24.

A. There is one solution, and it is (0, 2).

B. There are infinitely many solutions.

C. There is no solution.

D. There is one solution, and it is (–4, 1).

24. If the edge isn't included in the graph of an inequality, you should draw it as a/an _______ line.

A. dashed

B. solid

C. closed

D. open

25. Find the equation of the boundary line in the graph below. Then give the inequality represented by the

shaded area.

1. The matrix below is the augmented matrix of a system of three equations in the variables x and y. Solve

for x and y.

A. One solution,

B. One solution (0, 9)

C. No solution

D. Infinitely many solutions

2. Graph the following solution set:

x = y

2

y = x

3. Solve the inequality –2 (3 + x) < 4x + 4 < 8x. Give the result in set notation and graph it.

4. Solve the inequality |2x - 4| < 10. Write the solution in interval notation and graph it.

5. Graph the inequality 3x = –4y - 4.

6. Solve the inequality 4 < –z - 4 < 11. Give the result in set notation and graph it.

7. Which of the following phrases correctly describes the graph of the system of equations

and y = 2 - x?

A. The graph is of two parallel lines that do not intersect.

B. The graph is of two lines that coincide.

C. The graph is of two lines that intersect at a single point.

D. The graph is of a line and a parabola, which intersect at two points.

8. Are the two equations –6 + y = 2x and 2y - 4x = 12 dependent?

A. No, because the equations are not written the same.

B. No, because they are not parallel.

C. Yes, because they have the same graph.

D. Yes, because both are the equations of straight lines.

9. Solve the equation |6x + 3| = 15

A. x = 2

B. x = 4

C. x = –3

D. x = –3 or x = 2

10. Choose the correct ways to fill in the blanks in the following sentence.

To solve a system of equations using the matrix method, use __________ to transform the augmented

matrix into one with __________, then proceed to back-substitute.

A. the coefficient matrix, an inverse

B. the coefficient matrix, Gaussian elimination

C. multiplication and addition, zeros in its final column

D. elementary row operations, zeros below the diagonal

11. Solve the equation |x| = 7.

A. x = 7 or x = –7

B. x = 7

C. x = –7

D. Undefined

12. Solve the system of equations x + y + z = 9, –x + y + z = 1, and x - y - z = 5.

A. There is not enough information to solve the problem.

B. There is one solution, x = 4, y = 2, and z = 3.

C. There are infinitely many solutions.

D. There is no solution.

13. Graph the solution set of

x + 2y = 3

x + 2y = 4

14. Solve the inequality |5x + 10| = 15. Write the solution in interval notation and graph it.

15. Consider two ships, one on a course described by the equation 0.6x + 0.3y = 2.1 and the other on a

course described by the equation –0.3x + 0.1y = –1.8. Which of the following sentences best describes the

possibility of a collision?

A. There is a possibility of a collision at the point (5, –3) but a collision is not a certainty.

B. There is a possibility of a collision at the point (0, 7) but a collision is not a certainty.

C. There is no possibility for a collision.

D. There will certainty be a collision at the point (6, 0).

16. Graph the following solution set:

x + y = 4

x = 0

y = 0

A.

B.

C.

D.

17. Find the equation of the boundary line in the graph below. Then give the inequality represented by the

shaded area.

A.

B.

C.

D.

18. Graph the following solution set:

y = x - 1

y = 2x

A.

B.

C.

D.

19. Solve the inequality . Give the result in set notation and graph it.

A.

B.

C.

D.

20. Find the value of the expression –|–18|.

A. 18

B. –18

C. 0

D. Undefined

21. What is the formula for the determinant of a 3 x 3 matrix ?

22. Graph the inequality y < 3x + 1.

23. Solve the system of equations x - 4y = –8 and –3x + 12y = 24.

A. There is one solution, and it is (0, 2).

B. There are infinitely many solutions.

C. There is no solution.

D. There is one solution, and it is (–4, 1).

24. If the edge isn't included in the graph of an inequality, you should draw it as a/an _______ line.

A. dashed

B. solid

C. closed

D. open

25. Find the equation of the boundary line in the graph below. Then give the inequality represented by the

shaded area.

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