SAT Linear inequalities in one or two variables Practice Question 15 (Hard)

Question bank / Linear inequalities in one or two variables

Math · AlgebraHard

$y \le -2x + 10$
$y \ge x + 1$
In the $xy$ -plane, if the point $(a, b)$ lies in the solution region of the system of inequalities above, what is the greatest possible value of $a$ ?

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Answer: 3

A point in the region needs some $y$ with $x + 1 \le y \le -2x + 10$ , which requires $x + 1 \le -2x + 10$ . So $3x \le 9$ and $x \le 3$ . At $x = 3$ , $y = 4$ satisfies both inequalities, so the greatest value of $a$ is 3.

Answering 4 gives the $y$ -coordinate of the boundary intersection $(3, 4)$ , not the $x$ -coordinate.

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