# solving system of linear equations and linear inequalities

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1. Solve the system by graphing.

x + y = 4

-x + y = 2

2. Determine which two equations represent perpendicular lines.

3. Solve the system by graphing.

3x + y = 6

3x - y = 0

4. Graph the inequality y < -3

5. Solve the following system of linear inequalities by graphing.

x + 2y < = 3

2x - 3y <= 6

6. Anna has 12 bills in her wallet, some $5 and some $10. The total value of the bills is $100. How many of each bill does Anna have?

7. Determine which two equations represent parallel lines.

(a) y = -6x + 4 (b) y = 6x + 4 (c) y = 1/6 x + 4 (d) y = -6x + 5

8. Graph the solution set of x < -1.

9. Solve the following system of linear inequalities by graphing.

x - 2y >= 4

x < = 4

10. Solve. 8 - (4x - 3) = 19

11. Graph x = 3.

12. Find the slope and the y-intercept.

y = -9x

13. Find the slope of the graphed line.

14. Graph 3x + 2y = 6.

15. Solve the system by addition.

4x - 7y = 17

x - 5y = 1

16. Find the slope of the line passing through the points (-1, 1) and (-2, 9).

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2. When two line are ...

#### Solution Summary

The solution is comprised of detailed explanations using graphing as a tool to solve the system of linear equations and linear inequalities. Furthermore, the solution explains the line equations and how to determine the perpendicular and parallel lines from the line equations.