Which of the following ordered pairs is a solution to the system of inequalities above?

Question

Accepted Answer

Choice D is correct. The solutions to the given system of inequalities is the set of all ordered pairs that satisfy both inequalities in the system. For an ordered pair to satisfy the inequality , the value of the ordered pair&rsquo;s y -coordinate must be less than or equal to the value of the ordered pair&rsquo;s x -coordinate. This is true of the ordered pair , because . To satisfy the inequality , the value of the ordered pair&rsquo;s y -coordinate must be less than or equal to the value of the additive inverse of the ordered pair&rsquo;s x -coordinate. This is also true of the ordered pair . Because 0 is its own additive inverse, is the same as . Therefore, the ordered pair is a solution to the given system of inequalities. Choice A is incorrect. This ordered pair satisfies only the inequality in the given system, not both inequalities. Choice B incorrect. This ordered pair satisfies only the inequality in the system, but not both inequalities. Choice C is incorrect. This ordered pair satisfies neither inequality.

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