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Introduction to Algebra
Practice Test #4
Graph the equation in problems 1 through 4. Draw each one on a separate set of axes.
1. –3x + y = 1
2. y = 5
3. x = -2
4. y = (-1/3)x + 2
5. Graph the line that passes through the point (-3, 4) and has a y-intercept of 3.
6. Find the x-intercept of x – 3y = -2
7. Find the y-intercept of x – 3y = -2
8. Find the slope of the line which passes through (2, -3) and (5, 2).
9. Find the equation of the line for which m = ½ and b = -3.
10. Find the equation of the line which passes through (-3, 2) and for which m = -2.
11. Find the equation of the line which passes through (1, -2) and (-3, 2).
Solve the following systems by graphing. Draw each system on a separate set of axes.
12.
ì3x − y = 7
í
î2 x − y = 5
13.
ìx + 2 y = 8
í
î2 x − 3 y = 2
Solve the following systems by elimination. Show your work.
14.
ì2 x + y = 3
í
î3x + 2 y = 1
15.
ì− 2 x − 4 y = 1
í
î2 x + 4 y = −1
Solve the following systems by substitution. Show your work.
16.
ì x = −3 y − 1
í
î2 x − 3 y = 4
17.
ì− 3 x − 9 y = 7
í
î x + 3 y = 12
Solve by any method.
1
ì1
ïï 2 x − 3 y = 2
18. í
ï1 x + 2 y = 6
ïî 4
3
Solve the following word problems. Be sure to show the equations used.
19. The difference between two numbers is 7. Their sum is 35. Find the two numbers.
20. A total of $12,000 was invested. Part of the $12,000 was invested at 4% and rest was invested at 7%.
If the investments earn $600 in one year, how much was invested at each rate?
21. Find y such that the slope of the line containing (-2, 3) and (5, y) is 1/7.