ACT Preparation / Unit 9 ACT 0832 worked example, 60 to 90 seconds
Which Points Satisfy a System of Inequalities
The idea
To check whether a point lies in the solution region, work in three steps. First, substitute its coordinates into each inequality. Second, decide whether each statement is true, paying attention to whether the boundary is included. Third, the point is in the region only if every inequality is true; one false statement excludes it.
In practice
Worked example: y > 2x − 1 and x + y ≤ 6. The point (1, 3): 3 > 1 is true, and 4 ≤ 6 is true, so it is in the region. The point (3, 4): 4 > 5 is false, so it is out, whatever the second inequality says. The point (2, 4): 4 > 3 is true, and 6 ≤ 6 is true, so it lies in the region, on the solid boundary of the second.
Where people slip
A point exactly on a dashed boundary is outside the region, and one on a solid boundary is inside. The strict sign decides.
Your place on the trail
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Builds on
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