1. Section 7.5 Systems of Linear Inequalities

2. What You Will Learn
Solving Systems of Linear Inequalities

3. Solving a System of Linear Inequalities
1. Select one of the inequalities. Replace the inequality symbol with an equals sign and draw the graph of the equation. Draw the graph with a dashed line if the inequality is < or > and with a solid line if the inequality is ≤ or ≥.

4. Solving a System of Linear Inequalities
2. Select a test point on one side of the line and determine whether the point is a solution to the inequality. If so, shade the area on the side of the line containing the point. If the point is not a solution, shade the area on the other side of the line.

5. Solving a System of Linear Inequalities
3. Repeat Steps 1 and 2 for the other inequality.
4. The intersection of the two shaded areas and any solid line common to both inequalities form the solution set to the system of inequalities.

6. Example 1: Solving a System of Inequalities
Graph the following system of inequalities and indicate the solution set.

7. Example 1: Solving a System of Inequalities
Solution
Graph both inequalities on the same axes.
Begin with x + y < 1.

8. Example 1: Solving a System of Inequalities
Solution
Now graph x – y < 5.
The solution is in green.

9. Example 2: Solving a System of Inequalities
Graph the following system of inequalities and indicate the solution set.

10. Example 2: Solving a System of Inequalities
Solution
Graph both inequalities on the same axes.
Begin with 4x – 2y ≥ 8.

11. Example 2: Solving a System of Inequalities
Solution
Now graph 2x + 3y < 6.
The solution is in green.

12. Example 3: Another System of Inequalities
Graph the following system of inequalities and indicate the solution set.

13. Example 3: Another System of Inequalities
Solution
Graph both inequalities on the same axes.
Begin with x ≥ –2.

14. Example 3: Another System of Inequalities
Solution
Now graph y < 3.
The solution is in green.