y < -2x + 8 y x + c In the system of inequalities, c is a... | SAT Linear inequalities in one or two variables Question, Answer Explained

Question bank / Linear inequalities in one or two variables

Math · AlgebraHard

$y < -2x + 8$
$y > x + c$
In the system of inequalities, $c$ is a constant. If the point $(2, 3)$ is a solution to the system, which of the following must be true?

$c < -1$

$c > -1$

$c < 1$

$c > 1$

Show answer and explanation

Answer: C

The first inequality gives $3 < -2(2) + 8 = 4$ , which is true no matter what $c$ is. The second inequality requires $3 > 2 + c$ , so $c < 1$ . Values such as $c = 0$ and $c = -5$ both make $(2, 3)$ a solution, so neither choice A nor choice B has to be true.

Choice D reverses the inequality when solving $3 > 2 + c$ .

Why the other choices are wrong

A. c could be 0, which still makes (2, 3) a solution, so c < -1 doesn't have to be true.
B. c could be -5, which also makes (2, 3) a solution, so c > -1 doesn't have to be true.
D. This reverses the inequality. From 3 > 2 + c, subtracting 2 gives 1 > c.

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