Systems of Inequalities

Graphing Systems of Inequalities

Prentice Hall's Online Lesson Quiz Enter Web Code: aga–0303

Objective

In real-world situations there are often many conditions or constraints that need to be considered. Two or more linear inequalities for which a common solution is sought is called a system of inequalities.

Recall from Chapter 2, Section 7 the information needed to graph a linear inequality or re-read notes from this section.

Example 1:

Graph:

Graph the inequality ,
graphing the boundary line 2x + y = 8 (solid), and shading the half-plane above the boundary line.
Use for rapid graphing.

Graph the inequality , graphing the boundary line 2x – y > 1 (dashed), and shading the half-plane below the line in another color.
Use for rapid graphing.

The region where the shadings overlap is the graph of the solution to the system of inequalities.

In this example only the final solution set is shaded for understanding.

Example 2:

Graph:

Graph the inequality y < 3,
graphing the boundary line y = 3 (dotted), and shading the half-plane below the boundary line.

Graph the inequality , graphing the boundary line y = |x + 3 |– 2 (solid), and shading the half-plane above the line in another color.

The region where the shadings overlap is the graph of the solution to the system of inequalities.

In this example only the final solution set is shaded for understanding.

Example 2:
Graph: Graph the inequality y < 3, graphing the boundary line y = 3 (dotted), and shading the half-plane below the boundary line. Graph the inequality , graphing the boundary line y = \|x + 3 \|– 2 (solid), and shading the half-plane above the line in another color. The region where the shadings overlap is the graph of the solution to the system of inequalities.	In this example only the final solution set is shaded for understanding.