1. SYSTEMS OF LINEAR INEQUALITIES
Solving Linear Systems of Inequalities by Graphing

2. Solving Systems of Linear Inequalities
We show the solution to a system of linear inequalities by graphing them.
This process is easier if we put the inequalities into Slope-Intercept Form, y = mx + b.

3. Solving Systems of Linear Inequalities
Graph the line using the y-intercept & slope.
If the inequality is < or >, make the lines dotted.
If the inequality is < or >, make the lines solid.

4. Solving Systems of Linear Inequalities
The solution also includes points not on the line, so you need to shade the region of the graph:
above the line for ‘y >’ or ‘y ’.
below the line for ‘y <’ or ‘y ≤’.

5. Solving Systems of Linear Inequalities
Example:
a: 3x + 4y > - 4
b: x + 2y < 2
Put in Slope-Intercept Form:

6. Solving Systems of Linear Inequalities
Example, continued:
Graph each line, make dotted or solid and shade the correct area. a:
dotted
shade above b:
dotted
shade below

7. Solving Systems of Linear Inequalities
a: 3x + 4y > - 4

8. Solving Systems of Linear Inequalities
a: 3x + 4y > - 4
b: x + 2y < 2

9. Solving Systems of Linear Inequalities
a: 3x + 4y > - 4
b: x + 2y < 2
The area between the green arrows is the region of overlap and thus the solution.

10. PRACTICE
#1 on Worksheet  We will solve on the whiteboard together!
STEP 1: REARRANGE inequalities to look like y = mx + b
4x + 5y ≤ 2 y ≤ x + 3
-4x x (already done for you!)
5y ≤ -4x + 2
y ≤ -4/5x + 2/5

11. Practice (cont.) STEP 2: Graph each inequality like a linear equation.
STEP 3: Shade area where point values “work” (plug in, does it make sense?)

12. Practice (cont.) STEP 4: FIND THE COMMONLY SHADED AREA.
STEP 5: This is your final answer (only shade this part on final answer)
FINAL ANSWER

13. PRACTICE (cont) (#2)
3x + 5y > 15 y ≤ x – 2 -3x -3x already done!  5y > -3x y > -3/5 x + 3 Repeat graphing strategy (5 STEPS!)

14. PRACTICE
Solve # 3-8 on Worksheet by graphing on your whiteboard! 
(worksheet should be inside communicator!)