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Linear inequalities in one or two variables SAT question
Math · Algebra · Medium · Answer it here, explanation included.
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Which of the following ordered pairs (x, y) satisfies the system of inequalities above?
ExplanationShow
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 
. Of the given answer choices, only choice D satisfies this inequality, because inequality 
is a true statement. The point 
also satisfies the first inequality.
Alternate approach: Substituting into the first inequality gives 
, or 
, which is a true statement. Substituting into the second inequality gives 
, or 
, which is a true statement. Therefore, since 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 
, or 
, which is false. Choice B is incorrect because substituting −1 for x and 3 for y in the first inequality gives 
, or 
, which is false. Choice C is incorrect because substituting 1 for x and 5 for y in the first inequality gives 
, or 
, which is false.
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