PSAT Math Multiple-Choice Question 40: Answer and Explanation

Question: 40

2x - y > -3

4x + y < 5

y > -6

Which of the following points is in the solution set of the system of inequalities above?

• A. (-4, -1)
• B. (-3, -2)
• C. (-1, -1)
• D. (3, -5)

Correct Answer: C

Explanation:

C

The question asks for the point that satisfies a system of inequalities. There are specific points in the answers, so plug in the answers. Test the ordered pairs in each inequality from the question and look for a pair that makes all three inequalities true. Start by plugging (A) into the first inequality to get 2(-4) - (-1) > -3. This becomes -8 - (-1) > -3, or -7 > -3. Since this is not true, eliminate (A). Now plug the point in (B) into the first inequality to get 2(-3) - (-2) > -3. This becomes -6 - (-2) > -3, or -4 > -3. Since this is not true, eliminate (B). Now plug the point in (C) into the first inequality to get 2(-1) - (-1) > -3. This becomes -2 - (-1) > -3, or -1 > -3. This is true, but the point must work in all three inequalities. Plugging the point in (C) into the second inequality gives 4(-1) + (-1) < 5. This becomes -4 + (-1) < 5, or -5 < 5. This is true, but test the third inequality as well. Plugging the point in (C) into the third inequality gives -1 > -6. This is also true. The point in (C) satisfies all three inequalities in the system. The correct answer is (C).