Systems of Inequalities
Key rules for graphing, shading, and testing points in systems of linear inequalities.
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Questions Covered in This Set
11 cards to master
What does the graph of a single linear inequality represent?
A half-plane — the boundary line plus all points on one side of it.
When is a boundary line dashed vs. solid?
Dashed for strict symbols (< or >); solid for ≤ or ≥, where points on the line count.
If an inequality is solved for y, how do you know which side to shade?
y > or y ≥ shades above the line; y < or y ≤ shades below.
What is the test-point trick?
Plug an easy point not on the line (usually the origin) into the inequality; if it's true, shade that side.
What is the solution to a SYSTEM of inequalities?
The intersection (overlap) of all the shaded regions — the double-shaded area where every inequality is true.
Is (1, 4) a solution to y ≥ x + 1 and y < -2x + 6?
No. 4 ≥ 2 ✓, but 4 < 4 is false because the inequality is strict.
Fastest strategy for 'which point is a solution' questions?
Don't graph — plug the answer choices into the simpler inequality first to eliminate options.
Three elimination checks for 'which graph' questions?
(1) y-intercepts of boundaries, (2) dashed vs. solid, (3) which side is shaded (origin test).
What is a feasible region?
The overlapping shaded region of a real-world system showing every allowed combination.
Where do maximum or minimum values occur on a feasible region?
At a corner (vertex), found by solving the two boundary equations as a system.
What does x < 3 look like on a graph?
Everything to the left of a vertical dashed line at x = 3.
