PSAT Math Multiple-Choice Question 465: Answer and Explanation

Question: 465

One of the x-coordinates of the solutions to a system of equations is -8. Which of the following could be the system?

• A.
• B.
• C.
• D.

Correct Answer: D

Explanation:

D

Difficulty: Hard

Strategic Advice: Solving each system would be absurdly time-consuming. Backsolving will be faster.

Getting to the Answer: Substitute x = -8, the x-value at one of the points of intersection, into each equation. The correct system will have both equations equaling the same number, which is the y-value at that point of intersection. Look at each answer choice:

(A):

7 ≠ 253, so eliminate (A).

(B):

0 ≠ 17, so eliminate (B).

(C):

0 ≠ 23, so eliminate (C).

(D):

7 = 7, so the two equations in (D) intersect at the point (-8, 7). Thus, (D) is correct.