Inequalities in Two Variables
10-8Systems of Linear Inequalities
Overview
Graph each inequality. Solution region is the overlap of shaded areas.
Key ideas
- Use a different shading for each inequality.
- Solution = intersection of shaded regions.
- Check a point in the overlap.
Worked examples
Example 1
Problem. Graph: y ≥ x and y ≤ −x + 4.
Solution. Solid lines; shade above first, below second; overlap is a triangular region.
Practice
Try each one. Click Show answer when ready.
- 1.
Test (0, 0) in y > x AND y < x + 1: satisfy?
- 2.
Two inequalities with parallel lines—possible no overlap?
- 3.
Solution region of a system is always…
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Graph the system: y > x + 1 and y ≤ −x + 3.
- 2.
Graph the system: x ≥ 0, y ≥ 0, and x + y ≤ 5.