Systems of Inequalities

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 inequality • 1. • 2.

5. EX: Graph each inequality • 3. • 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 system • 6.

8. EX: Graph the solution set of the system • 7.

9. EX: Graph the solution set of the system • 8.

10. EX: Write a system of linear inequalities that has the given graph • 9.