PSAT Math Multiple-Choice Question 241: Answer and Explanation

Question: 241

The x-coordinates of the solutions to a system of equations are - 4 and 2. Which of the following could be the system?

• A.
• B.
• C.
• D.

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Passport to Advanced Math/Quadratics

Getting to the Answer: The solution to a system of equations is the point(s) where their graphs intersect. You could solve this question algebraically, one system at a time, but this is not time efficient. Instead, graph each pair of equations in your graphing calculator and look for the graphs that intersect at x = - 4 and x = 2. The graphs of the equations in (A) and (B) don't intersect at all, so you can eliminate them right away. The graphs in (C) intersect, but both points of intersection have a positive x-coordinate. This means (D) must be correct. The graph looks like this: