SAT Linear inequalities in one or two variables Practice Question 11 (Medium)

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Question bank / Linear inequalities in one or two variables

Math · AlgebraMedium

For which of the following systems of inequalities is the point $(2, 3)$ a solution?

$y > x + 2$
$y < 4$

$y \le -x + 4$
$y \ge 0$

$y \ge 2x$
$x + y \le 4$

$y < x + 2$
$y > 1$

Show answer and explanation

Answer: D

Substitute $x = 2$ and $y = 3$ . In choice D, $3 < 2 + 2 = 4$ is true and $3 > 1$ is true, so $(2, 3)$ satisfies both inequalities. Each other system has an inequality that fails: $3 > 4$ , $3 \ge 4$ , and $3 \le 2$ are all false.

Choice B satisfies $y \ge 0$ , but $3 \le -2 + 4 = 2$ is false, so the point fails the first inequality.

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