For which of the following inequalities are both (0, 0) and... | SAT Linear inequalities in one or two variables Question, Answer Explained

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For which of the following inequalities are both $(0, 0)$ and $(3, -1)$ solutions?

$y > x - 2$

$y < -x + 1$

$y \ge -x$

$y \le 2x - 1$

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Answer: C

Test both points in each inequality. For $y \ge -x$ : at $(0, 0)$ , $0 \ge 0$ is true, and at $(3, -1)$ , $-1 \ge -3$ is true. So both points are solutions of choice C. Each of the other inequalities fails for at least one of the points.

Choice A works for $(0, 0)$ but fails for $(3, -1)$ , since $-1 > 1$ is false.

Why the other choices are wrong

A. (0, 0) works, but at (3, -1) it says -1 > 1, which is false.
B. (0, 0) works, but at (3, -1) it says -1 < -2, which is false.
D. At (0, 0) it says 0 ≤ -1, which is false.

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