SAT Linear inequalities in one or two variables Practice Question 20 (Hard)

Question bank / Linear inequalities in one or two variables

Math · AlgebraHard

$y \ge 2x - 7$
$y < -x + 9$
The point $(5, k)$ lies in the solution set of the system of inequalities above. Which of the following could be the value of $k$ ?

$2$

$3$

$4$

$5$

Show answer and explanation

Answer: B

At $x = 5$ , the first inequality gives $k \ge 2(5) - 7 = 3$ , and the second gives $k < -5 + 9 = 4$ . So $3 \le k < 4$ . Only $k = 3$ is among the choices.

Choice C fails because the second inequality is strict: $4 < 4$ is false.

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