College Algebra Questions
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algebra_-_050353.pdf
Student ID: 21772952
Exam: 050353RR - SYSTEMS OF EQUATIONS; INEQUALITIES
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Questions 1 to 25: Select the best answer to each question. Note that a question and its answers may be split across a page break, so be sure that you have seen the entire question and all the answers before choosing an answer.
1. Graph the solution set of x + 2y ≤ 3 x + 2y ≤ 4
A.
B.
C.
D.
2. 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
3. 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.
4. 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).
5. Graph the inequality y ≥ –3.
A.
B.
C.
D.
6. Solve the equation |6x + 3| = 15 A. x = –3 or x = 2
B. x = 4
C. x = 2
D. x = –3
7. When solving the system of equations 6x + 2y = –1 and –x + 10y = 5 by Cramer's Rule, what are the values of D, D
x , and D
y ?
A. D = 58, D x = –20, D
y = –29
B. D = 62, Dx = 20, Dy = 28
C. D = 58, D x = 20, D
y = –28
D. D = 62, Dx = –20, Dy = 29
8. Graph the following solution set: y ≤ x − 1 y ≥ 2x
A.
B.
C.
D.
9. Graph the following solution set: x + y ≤ 4 x ≥ 0 y ≥ 0
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B.
C.
D.
10. Graph the following solution set:
x ≤ y2 y ≥ x
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B.
C.
D.
11. Solve the inequality . Give the result in set notation and graph it.
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B.
C.
D.
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 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.
13. Find the equation of the boundary line in the graph below. Then give the inequality represented by the shaded area.
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B.
C.
D.
14. Graph the inequality y < 3x + 1.
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B.
C.
D.
15. Use matrices to help find a general solution for this system of equations. 2x − y + 3z = 5 –x + 4y + 4z = –1
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B.
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D.
16. 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 no possibility for a collision.
B. There is a possibility of a collision at the point (5, –3) but a collision is not a certainty.
C. There is a possibility of a collision at the point (0, 7) but a collision is not a certainty.
D. There will certainty be a collision at the point (6, 0).
17. The first two rows of the following matrix are already in triangular form. Finish the job by performing Gaussian elimination on row 3. What are the contents of row 3 after you have done so?
.
A. 0 0 3 29
B. 0 0 1 9
C. 0 0 3 –11
D. 0 0 –5 –11
18. 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
19. Solve the inequality . Give the result in set notation and graph it.
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B.
C.
D.
20. Convert to a fraction.
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B.
C.
D.
21. Solve the system of equations y = 0.6x + 0.2 and 3x − 5y = 4. A. There are infinitely many solutions.
B. There is one solution, and it is .
C. There is one solution, and it is (0, 0.2).
D. There is no solution.
22. 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 no solution.
D. There is not enough information to solve the problem.
23. Solve the inequality |2x − 4| < 10. Write the solution in interval notation and graph it.
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B.
C.
D.
24. Which of the following ordered pairs is a solution to the system of equations y = x − 6 and 2y = –x + 14?
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B.
C.
D.
25. Solve the inequality |5x + 10| ≥ 15. Write the solution in interval notation and graph it.
A.
End of exam
B.
C.
D.
