Name_________________________________
Algebra 1
Unit 6 Review
1. Is (-2, 3) a solution to the following system? y = -x + 1 y = ½x + 4
2. Is (4, -1) a solution to the following system? 3x + y > 8
x – 2y < 4
For problems 3 - 6 state determine how many solutions the system has.
3. y = 3x + 1
y = 3x + 1
4. y = ⅓x + 6
y = ⅓x – 2
5. y = ½x – 4 6. 10x – 4y = 12
y = ¼x + 9 5x – 2y = 6
7. 3x – 7y = 10
-9x + 21y = 15
8.
Multiple choice: At what point do the lines defined by the equations x + y = 15 and x – y = -1 intersect?
A (10, 5) B
12
5
,
1
5
C (-1, 15) D (7, 8)
In 9 – 10, solve the systems of equations by graphing.
9. y = x + 1 10 . y = -2x - 6
y =
2
5 x + 4 y

3
4 x

5
In 11 - 13, solve the systems of equations by the substitution method.
11. x = y – 3 12. 3x – 4y = -11
4x + 2y = 48 y = 2x - 1
13. y = 4x – 13
y = -x – 3

In 14 - 16, solve the systems of equations by the addition/elimination method.
14. 2x + 4y = -14 15. 3x – 2y = 6 16. 4x + 3y = 23
3x – 4y = 9 6x + 5y = 12 7x – 2y = 4
Chapter 2, 3, and 5 Review
Solve the following equations.
20.
2
3 x + 2 = 20 21. 2(3x + 4) – 3 = -13 22. x
5

4
 x
2

6 x
23.
3

3
5

2
3
24.
3 x
4
 x
2

5 25. 2 x

1

7 26. x

8

5

9
For problems 27 – 29, state whether the equation has one solution, no solutions, or if it is an
Identity (Infinitely Many Solutions)
27. 4(x – 3) = 4x – 12 28. 10x – 3x – 9 =4 29. 2x + 6(x + 1) = 4(2x – 3)
30. Find the x-intercept and the and y-intercept : 2x + 3y = 12
31. Find the slope and y-intercept : x – 4y = 8
32. Write the equation for the line containing the point (6, -1) that has slope of

1
2
.
33. Find the equation of the line that passes through the points (2, 7) and (-4, -5).
34. Find the equation of the line that passes through the point (-2, -7) that is parallel to the line y = 3x + 1.
35. Are the two lines 3x – y = -7 and x + 3y = 6 parallel or perpendicular?