SAT Math: Systems of Inequalities
22+ practice questions in Praczo
The concept, explained
- 1
The solution to a system of inequalities is the region where the shaded areas of all inequalities overlap.
- 2
A solid line means the boundary is included (≤ or ≥). A dashed line means the boundary is excluded (< or >).
- 3
To verify which region is the solution, test a point (often (0,0)). If it makes all inequalities true, it is in the solution region.
- 4
When shaded regions are shown on a graph, the SAT might ask you to identify a point that satisfies the system — just look for a point in the doubly shaded overlap.
- 5
If you multiply or divide an inequality by a negative number, you must flip the inequality sign. This affects which side is shaded.
- ✗ Picking a point that satisfies only one inequality instead of both (a point outside the overlapping region).
- ✗ Selecting a point on a dashed boundary line, thinking it is part of the solution set.
SAT-style practice
Is the point (2, 3) a solution to the system: y > x + 1 and y ≤ −x + 6?
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