Understanding Systems of Inequalities
A system of inequalities consists of two or more inequalities that must be satisfied simultaneously. The solution is the region where all inequalities are true.
Key Concepts
- Use solid lines for ≤ or ≥
- Use dashed lines for < or >
- Shade regions that satisfy each inequality
- Solution is the overlap of all shaded regions
Important Steps:
- Graph each inequality separately
- Identify the overlapping region
- Test points to verify the solution
Solving Process
- 1
Graph Each Inequality
Draw each boundary line with appropriate style (solid/dashed).
- 2
Shade Valid Regions
Use test points to determine which side to shade.
- 3
Find Overlap
Identify region satisfying all inequalities.
- 4
Verify Solution
Test points in and out of the solution region.