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. Systems of Linear Inequalities
Graph the solution set of the system.
The solution set of the system of equations is the region shaded both red and green, including part of the line x + y  3.

10. 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.

11. x – 3y < 6
2x + 3y > -6 y x 10
-10

12. y > x2 – 4
x + y < 2 y x 10
-10