sat suite question viewer
Which of the following ordered pairs is a solution to the system of inequalities above?
Explanation
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’s y-coordinate must be less than or equal to the value of the ordered pair’s x-coordinate. This is true of the ordered pair
, because
. To satisfy the inequality
, the value of the ordered pair’s y-coordinate must be less than or equal to the value of the additive inverse of the ordered pair’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.