# File 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 8.

Multiple choice:

At what point do the lines defined by the equations x + y = 15 and x – y = -1 intersect? 7. 3x – 7y = 10 -9x + 21y = 15 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 4x + 2y = 48 12. 3x – 4y = -11 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 3x – 4y = 9 15. 3x – 2y = 6 16. 4x + 3y = 23 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?