Solve systems of linear inequalities by graphing

Find feasible regions by overlapping shaded half-planes.

Lesson 2

Concept

Graph each inequality and shade its solution region. The system solution set is the overlapping region.

Graph y ≥ x - 2 and y < -x + 4. Describe the feasible region.

System-inequality solutions appear where shading:

Does not overlap

Overlaps

Touches only axes

Is random

A strict inequality boundary is drawn as:

Solid line

Dashed line

Double line

No line

These steps are out of order — can you fix them?

1.Find overlap region

2.Test a point in overlap

3.Shade each valid side

4.Graph each boundary with correct line type

How can you verify a feasible-region point quickly?