Exam: 050291RR - Systems of Equations; Inequalities
1. Graph the following solution set:
y = x - 1
y = 2x
2. Solve the inequality –6 = 6x < 24. Give the result in set notation and graph it.
3. Solve the equation |6x + 3| = 15
4. Solve the inequality |2x - 4| < 10. Write the solution in interval notation and graph it.
5. Graph the inequality 3x = –4y - 4.
A.
B.
6. What is the formula for the determinant of a 3 x 3 matrix ?
7. Solve the system of equations x - 4y = –8 and –3x + 12y = 24.
A. There is one solution, and it is (–4, 1).
B. There is one solution, and it is (0, 2).
C. There is no solution.
D. There are infinitely many solutions.
8. Find the equation of the boundary line in the graph below. Then give the inequality represented by the shaded area.
B.
C.
9. When solving the system of equations 6x + 2y = –1 and –x + 10y = 5 by Cramer's Rule, what are the
A. D = 62, D
B.
D = 62, D
C. D = 58, D
D.
10. Graph the following solution set:
x + y = 4
x = 0
y = 0
11. 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 (0, 9)
B. No solution
C. One solution,
D. Infinitely many solutions
12. Solve the system of equations 2x - 2y - 2z = 3, x + 4y - z = 2, and –2x - 8y + 2z = –4.
A. There are infinitely many solutions, of the form (x, 0.1, x -1.6).
B. There is no solution.
C. There are infinitely many solutions, of the form (0.1, 0.1, –1.5).
D.
There is one solution, (0.1, 0.1, –1.5).
13. Are the two equations –6 + y = 2x and 2y - 4x = 12 dependent?
A. Yes, because they have the same graph.
B. No, because they are not parallel.
C. No, because the equations are not written the same.
D. Yes, because both are the equations of straight lines.
14. Graph the inequality y = –3.
A.
B.
C.
D.
15. Solve the system of equations 2x - y + z = –7, x - 3y + 4z = –19, and –x + 4y - 3z = 18.
A. There is one solution, (–1, 2, –3).
B.
There is one solution, (–1, –2, –3).
C. There is one solution, (1, –2, 3).
D.
There is one solution, (1, 2, 3).
16. Solve the inequality . Give the result in set notation and graph it.
A.
B.
C.
D.
17. Solve the inequality –2 (3 + x) < 4x + 4 < 8x. Give the result in set notation and graph it.
A.
B.
C.
D.
18. Graph the inequality y < 3x + 1.
A.
B.
C.
D.
19. Graph the following solution set:
x = y
y = x
A.
B.
C.
D.
2
20. Solve the equation |x| = 7.
A. Undefined
B. x = 7
C. x = 7 or x = –7
D. x = –7
21. Find the equation of the boundary line in the graph below. Then give the inequality represented by the
shaded area.
A.
B.
C.
D.
22. Find the value of the expression –|–18|.
A. 18
B. –18
C. Undefined
D. 0
23. Solve the system of equations x + y + z = 9, –x + y + z = 1, and x - y - z = 5.
A. There are infinitely many solutions.
B. There is one solution, x = 4, y = 2, and z = 3.
C. There is not enough information to solve the problem.
D. There is no solution.
24. When solving a system of equations using Cramer's Rule, if D
x
= 0, D
y
= –1, D
= 1, and D = 0, then
what can you conclude?
A. The system is dependent.
B. The system has one solution, (0, –1, 1).
C. The system is inconsistent.
D. The system has one solution, (0, 0, 0).
25. Which of the following phrases correctly describes the graph of the system of equations
and y = 2 - x?
A. The graph is of a line and a parabola, which intersect at two points.
B. The graph is of two lines that coincide.
C. The graph is of two parallel lines that do not intersect.
D. The graph is of two lines that intersect at a single point.
