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. Example:
3y < 2x - 8
y > (2/3) x - 1

11. Analyzing situations and formulate systems of inequalities to solve problems.
A charity is selling T-shirts in order to raise money. The cost of a T-shirt is $ 15 for adults and $ 10 for students. The charity needs to raise at least $3000 and has only 250 T-shirts. Write and graph a systems of inequalities that can be used to determine the number of adult and student T-shirts the charity must sell.