Exam: 050291RR - Systems of Equations; Inequalities
1. Find the equation of the boundary line in the graph below. Then give the inequality represented by the
shaded area.
2. Graph the solution set of
x + 2y = 3
x + 2y = 4
3. 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. elementary row operations, zeros below the diagonal
C. multiplication and addition, zeros in its final column
4. Aunt Jane's Pies had a tent at the county fair. Unfortunately their cash register broke, so they have no receipts. They know from counting their left over paper plates that they made 413 sales. They know from the cash box that they made $2,243. If they only sell two kinds of items at the fair tent, a piece of pie for
$4 and pie á là mode for $7, help them figure out how many of each kind they sold.
A. The system of equations is inconsistent, and therefore their plate counting or money counting must have an error.
B. They sold 216 pieces of pie and 197 pies á là mode.
C. They sold 355 pieces of pie and 58 pies á là mode.
D. They sold 610 pieces of pie and 4683 pies á là mode.
5. Solve the inequality . Give the result in set notation and graph it.
6. Graph the following solution set:
y = x - 1
y = 2x
7. Solve the inequality –6 = 6x < 24. Give the result in set notation and graph it.
8. Solve the inequality . Give the result in set notation and graph it.
9. Are the two equations –6 + y = 2x and 2y - 4x = 12 dependent?
A. Yes, because both are the equations of straight lines.
B. Yes, because they have the same graph.
C. No, because they are not parallel.
D. No, because the equations are not written the same.
10. Solve the equation |x| = 7.
A. x = 7
B. x = 7 or x = –7
C. Undefined
D. x = –7
11. 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 a line and a parabola, which intersect at two points.
C. The graph is of two lines that coincide.
D. The graph is of two lines that intersect at a single point.
12. Solve the system of equations x + y + z = 9, –x + y + z = 1, and x - y - z = 5.
A. There is no solution.
B. There is one solution, x = 4, y = 2, and z = 3.
C. There are infinitely many solutions.
D. There is not enough information to solve the problem.
13. Graph the following solution set:
x + y = 4
x = 0
y = 0
14. 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 is inconsistent.
C. The system has one solution, (0, 0, 0).
D. The system has one solution, (0, –1, 1).
15. Solve the system of equations 2x - 2y - 2z = 3, x + 4y - z = 2, and –2x - 8y + 2z = –4.
z
A. There are infinitely many solutions, of the form (0.1, 0.1, –1.5).
B. There are infinitely many solutions, of the form (x, 0.1, x -1.6).
C. There is one solution, (0.1, 0.1, –1.5).
D. There is no solution.
16. Graph the inequality y < 3x + 1.
17. If the edge isn't included in the graph of an inequality, you should draw it as a/an _______ line.
A. solid
B. dashed
C. open
D. closed
18. Solve the system of equations x - 4y = –8 and –3x + 12y = 24.
A. There is one solution, and it is (0, 2).
B. There is no solution.
C. There is one solution, and it is (–4, 1).
D. There are infinitely many solutions.
19. 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).
20. Find the equation of the boundary line in the graph below. Then give the inequality represented by the
shaded area.
21. Graph the inequality 3x = –4y - 4.
22. Solve the inequality 4 < –z - 4 < 11. Give the result in set notation and graph it.
23. Solve the equation |6x + 3| = 15
A. x = 4
B. x = –3 or x = 2
C. x = 2
D. x = –3
24. Solve the inequality –2 (3 + x) < 4x + 4 < 8x. Give the result in set notation and graph it.
25. Solve the inequality |5x + 10| = 15. Write the solution in interval notation and graph it.
