1. Systems of Inequalities
Objectives:
Graph an Inequality
Graph a System of Linear Inequalities

2. Graphs of an Inequality
Graph of an Inequality in two variables: consists of all points whose coordinates satisfy the inequality
Half-plane: the set of all the points on one side of a line
a solid line is used to show that a line is part of the graph
a dashed line is used to show that a line is not part of the graph

3. Steps for graphing an Inequality in two variables
1. Replace the inequality symbol with an equal sign and graph the corresponding equation. Draw a solid line if the original inequality contains symbols. Draw a dashed line if the original inequality contains symbols.
2. Choose a test point form one of the half-planes. (Do not choose a point on the line.) Substitute the coordinates of the test point into the inequality.
3. If a true statement results, shade the half-plane containing the test point. If a false statement results, shade the half-plane not containing this test point.

4. EX: Graph each inequality1. 2.

5. EX: Graph each inequality3. 4. 5.

6. Graph of a System of Inequalities
Graph of a System of Inequalities: the set of all points that simultaneously satisfy each of the inequalities in the system
To graph a system of inequalities in two variables, begin by graphing each individual inequality in the same rectangular coordinate plane. Then find the region, if there is one, that is common to every half-plane in the system. This region of intersection gives a picture of the system’s solution set.

7. EX: Graph the solution set of the system6.

8. EX: Graph the solution set of the system7.

9. EX: Graph the solution set of the system8.

10. EX: Write a system of linear inequalities that has the given graph9.