SAT Systems of Inequalities: The Desmos Shading Trick
Inequality questions ask which point lies in a region. Desmos shades each inequality, and the overlap is your answer set.
Step by step
- 1
Type each inequality on its own line
Use <, >, ≤, or ≥ exactly as written — e.g. y > x + 1 and y < −x + 5. Desmos shades each one.
- 2
Find the overlap
The region shaded by BOTH inequalities — the darker, double-shaded area — is the solution set. Every point there satisfies the whole system.
- 3
Test a point
To check whether a given point is a solution, just see if it lands inside the double-shaded region.
- 4
Watch solid vs dashed edges
A solid boundary (≤ or ≥) includes the line; a dashed boundary (< or >) does not.
- 5
Answer the question
Which point is a solution, or which region is described — both are visible at a glance.
Pro tip
When the question gives you answer-choice points, skip the algebra — just see which point sits inside the overlap region.
Try it yourself
Work the example right here in a live Desmos calculator — no Bluebook needed.
Which point satisfies both y > x + 1 and y < −x + 5: (0, 4) or (3, 3)?
Both points are plotted — see which one sits inside the double-shaded overlap.
Loading interactive calculator…
Show the answer
Answer: (0, 4)
Graph both inequalities; (0, 4) sits in the double-shaded overlap and (3, 3) does not. (Check: at (3, 3), 3 > 3 + 1 is false.)
Put the trick to work on a real test
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