1. Find the equation of the boundary line in the graph below. Then give the inequality represented by the shaded area.
2. 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. They sold 216 pieces of pie and 197 pies á là mode.
B. They sold 355 pieces of pie and 58 pies á là mode.
C. They sold 610 pieces of pie and 4683 pies á là mode.
D. The system of equations is inconsistent, and therefore their plate counting or money counting must have an error.
3. Solve the inequality . Give the result in set notation and graph it.
3. Solve the inequality . Give the result in set notation and graph it.
5. Find the equation of the boundary line in the graph below. Then give the inequality represented by the shaded area.
6. Graph the inequality y < 3x + 1.
7. Solve the inequality . Give the result in set notation and graph it.
8. Solve the inequality |2x − 4| < 10. Write the solution in interval notation and graph it.
9. 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. multiplication and addition, zeros in its final column
B. the coefficient matrix, an inverse
C. elementary row operations, zeros below the diagonal
D. the coefficient matrix, Gaussian elimination
10. Are the two equations –6 + y = 2x and 2y − 4x = 12 dependent?
A. No, because the equations are not written the same.
B. Yes, because both are the equations of straight lines.
C. Yes, because they have the same graph.
D. No, because they are not parallel.
11. Solve the equation |x| = 7.
A. x = 7 or x = –7
B. Undefined
C. x = 7
D. x = –7
12. 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. Infinitely many solutions
B. One solution,
C. One solution (0, 9)
D. No solution
13. Solve the equation |6x + 3| = 15
A. x = 2
B. x = –3 or x = 2
C. x = 4
D. x = –3
14. Graph the following solution set:
x ≤ y2
y ≥ x
15. Find the value of the expression –|–18|.
A. 18
B. Undefined
C. –18
D. 0
16. Which of the following phrases correctly describes the graph of the system of equations and y = 2 − x?
A. The graph is of two lines that coincide.
B. The graph is of two lines that intersect at a single point.
C. The graph is of two parallel lines that do not intersect.
D. The graph is of a line and a parabola, which intersect at two points.
17. Solve the system of equations x − 4y = –8 and –3x + 12y = 24.
A. There is no solution.
B. There is one solution, and it is (0, 2).
C. There is one solution, and it is (–4, 1).
D. There are infinitely many solutions.
18. Graph the inequality y ≥ –3.
19. If the edge isn't included in the graph of an inequality, you should draw it as a/an _______ line.
A. solid
B. closed
C. open
D. dashed
20. Graph the following solution set:
x + y ≤ 4
x ≥ 0
y ≥ 0
21. 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 one solution, (0.1, 0.1, –1.5).
C. There are infinitely many solutions, of the form (0.1, 0.1, –1.5).
D. There is no solution.
22. Graph the inequality 3x ≤ –4y − 4.
23. Graph the following solution set:
y ≤ x − 1
y ≥ 2x
24. Graph the solution set of
x + 2y ≤ 3
x + 2y ≤ 4
25. Solve the inequality –2 (3 + x) < 4x + 4 < 8x. Give the result in set notation and graph it.
