PSAT Math Multiple-Choice Question 102: Answer and Explanation

Question: 102

Which of the following ordered pairs (x, y) satisfies both equations and y = x² - 5x + 6?

• A. (0, 3)
• B. (2, -2)
• C. (4, 2)
• D. (6, 12)

Correct Answer: C

Explanation:

C

The question asks for the point that satisfies a system of equations. There are specific points in the answers, so use PITA. Test the ordered pairs in both equations from the question and look for a pair that makes both equations true. Start by plugging (A) into the first equation to get 0 = (3) + 3. This becomes 0 = + 3. Since this is not true, eliminate (A). Now plug the point in (B) into the first equation to get 2 = (-2) + 3. This becomes 2 = -1 + 3 or 2 = 2. This is true, but the point must work in both equations. Plugging the point in (B) into the second equation gives -2 = (2)² - 5(2) + 6, which becomes -2 = 4 - 10 + 6 or -2 = 0. Eliminate (B). Plug the point in (C) into the first equation to get 4 = (2) + 3. This becomes 4 = 1 + 3 or 4 = 4. This is true, but test the second equation as well. This gives 2 = (4)² - 5(4) + 6, which becomes 2 = 16 - 20 + 6 or 2 = 2. This is also true. The correct answer is (C).