Interactive applet
Systems of Linear Inequalities
Shade two half-planes. The overlap is the solution set. Drag a test point to check an ordered pair.
Hands-on lab
Shade · drag the test point
Blue is inequality 1. Coral is inequality 2. Where they stack is the solution set.
Inequality 1
y ≥ 0.5x − 1
Inequality 2
y ≤ -1x + 4
Test point
(2, 1) is in the overlap.
Satisfies inequality 1. Satisfies inequality 2.
Missions
- Shade above the first line (≥ or >)
- Park a test point in the overlap
- Use a dashed boundary (strict > or <)
- Make the overlap empty (no solution)
2/4 complete
Guided questions
A solid boundary is included (≥ or ≤). A dashed boundary is not (> or <). Why?
Reflection
Why is the solution of a system of inequalities a region, not a single point?
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