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Algebra / Linear inequalities in one or two variables Difficulty: Medium

$y is less than or equal to, 3 x plus 1$

$x minus y is greater than 1$

Which of the following ordered pairs (x, y) satisfies the system of inequalities above?

$negative 2 comma negative 1$

$negative 1 comma 3$

$1 comma 5$

$2 comma negative 1$

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Explanation

Choice D is correct. Any point (x, y) that is a solution to the given system of inequalities must satisfy both inequalities in the system. The second inequality in the system can be rewritten as $x is greater than, y plus 1$ . Of the given answer choices, only choice D satisfies this inequality, because inequality $2 is greater than, negative 1 plus 1$ is a true statement. The point $with coordinates 2 comma negative 1$ also satisfies the first inequality.

Alternate approach: Substituting $the ordered pair 2 comma negative 1$ into the first inequality gives $negative 1 is less than or equal to, 3 times 2, plus 1$ , or $negative 1 is less than or equal to 7$ , which is a true statement. Substituting $the ordered pair 2 comma negative 1$ into the second inequality gives $2 minus negative 1, is greater than 1$ , or $3 is greater than 1$ , which is a true statement. Therefore, since $the ordered pair 2 comma negative 1$ satisfies both inequalities, it is a solution to the system.

Choice A is incorrect because substituting −2 for x and −1 for y in the first inequality gives $negative 1 is less than or equal to, 3 times negative 2, plus 1$ , or $negative 1 is less than or equal to negative 5$ , which is false. Choice B is incorrect because substituting −1 for x and 3 for y in the first inequality gives $3 is less than or equal to, 3 times negative 1, plus 1$ , or $3 is less than or equal to negative 2$ , which is false. Choice C is incorrect because substituting 1 for x and 5 for y in the first inequality gives $5 is less than or equal to, 3 times 1, plus 1$ , or $5 is less than or equal to 4$ , which is false.