PSAT Math Grid-Ins Question 101: Answer and Explanation

Question: 101

What is the absolute difference of the values of x for the solutions to the system of equations above?

Correct Answer: 9

Explanation:

9

Difficulty: Hard

Category: Systems of Quadratic and Linear Equations

Getting to the Answer: Rearrange both equations to isolate y in terms of x:

Set both equations equal to each other to find where they intersect. Combine like terms on one side of the equation:

This quadratic equation can be solved by factoring since two factors of -14, 7 and -2, add to 5. Hence, (x + 7)(x - 2) = 0 and x = -7 and x = 2. The question asks for the absolute difference, so subtract the roots and evaluate as an absolute value:

Grid in 9.