Which of the following consists of the y -coordinates of all the points that satisfy the system of inequalities above?

Question

Accepted Answer

Choice B is correct. Subtracting the same number from each side of an inequality gives an equivalent inequality. Hence, subtracting 1 from each side of the inequality gives . So the given system of inequalities is equivalent to the system of inequalities and , which can be rewritten as . Using the transitive property of inequalities, it follows that . Choice A is incorrect because there are points with a y -coordinate less than 6 that satisfy the given system of inequalities. For example, satisfies both inequalities. Choice C is incorrect. This may result from solving the inequality for x , then replacing x with y . Choice D is incorrect because this inequality allows y -values that are not the y -coordinate of any point that satisfies both inequalities. For example, is contained in the set ; however, if 2 is substituted into the first inequality for y , the result is . This cannot be true because the second inequality gives .

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