1. Warm Up
Solve by graphing y = x + 3
2x + y = 4
2) Solve by substitution 2x + y = 5
4x + 2y = 5
3) Solve by elimination x – y = 7
3x – y = -19
Turn in stamp sheets today!

2. HW Check – 5.10 a) no solution b) no solution c) (2,3) d) (2, 2)
2) a) (9, 28) b) n = 1, C = -3
c) a = .75, b = d) s = -3, t = 9.4
3) a) (1, 3) b) (2, -2)

3. Graphing
Linear
Inequalities

4. We show the solution to a linear inequality with a graph.
Step 1) Put the inequalities into slope-intercept form.
y = mx + b
slope
y-intercept

5. Step 2) Graph the line
If the inequality is < or >, make the lines dotted.
If the inequality is < or >, make the lines solid.

6. Step 3) Shade the correct region of the graph:
Above the line b) Below the line
for y > or y . for y < or y ≤.
**This is because more then 1 ordered pair can be a solution!

7. Examples:
1) y > -5x + 4

8. Examples:
2) x < ) y ≥ -3

9. Examples:
4) 2x – 3y ≤ 6
**When you multiply or divide by a negative, flip the inequality sign.

10. Examples:
5) 3x + 2y < -2

11. Systems of
Inequalities

12. We show the solution to a system of linear inequalities with a graph!

13. Steps to Graphing a System of Inequalities:
Put the inequalities into slope-intercept form.
Decide if the lines should be dotted or solid
Shade above for y > or y , shade below for y < or y ≤.
Shade the overlapping section darker to show where the solutions to both inequalities lie.

14. Example #1: a: 3x + 4y > - 4 b: x + 2y < 2 Put in Slope-Intercept Form:

15. Graph each line, make dotted or solid and shade the correct area.
Example, continued:
Graph each line, make dotted or solid and shade the correct area.
a: dotted shade above
b: dotted shade below

17. #2 Graph the system of linear inequalities.
x ³ –1
y > x – 2

18. #3 x > -2 y < 6 -2x + y > -5

19. Let’s graph the next problem using the calculator #4 y ≥ -x + 4 y < 3x - 2

20. #5
x – y > 3 7x – y ≤ -3

21. #6
7x + 2y < -10 -x + 2y ≤ 11

22. Classwork: Solving Systems of Inequalities Worksheet Homework: 5.11