System of linear inequalities: y > x − 2 and y ≤ −x + 3

An example figure from the Coordinate Grid Generator.

A coordinate grid from −6 to 6 with the region above the dashed line y = x − 2 shaded blue and the region below the solid line y = −x + 3 shaded red, overlapping on the left — A coordinate grid numbered from −6 to 6 on both axes with two inequalities shaded. Above the dashed line y = x − 2 is shaded blue, dashed because points on it don’t make y > x − 2 true; below the solid line y = −x + 3 is shaded red, solid because points on it make y ≤ −x + 3 true. The lines cross at (2.5, 0.5), and the solutions to the system are where the shading overlaps, to the left of that point.

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Answer key

y > x − 2
y ≤ −x + 3

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