PSAT Math Multiple-Choice Question 466: Answer and Explanation

Question: 466

Which system of equations has only one solution?

• A.
• B.
• C.
• D.

Correct Answer: D

Explanation:

D

Difficulty: Hard

Strategic Advice: All of the choices present a system of equations that includes a parabola and a line. For a system of equations to have only one solution, the graphs must have only one point of intersection.

Getting to the Answer: Notice that all of the choices have the same parabola with a vertex of (-3, -5). Choices (B) and (D) have horizontal lines, which are easy to check. Choice (B) has a horizontal line at y = 5, but with the parabola facing downward, the parabola will never intersect it. Choice (D) has a horizontal line at y = -5, which is where the parabola's vertex lies. This means the line is tangent to the parabola and will touch the parabola only once to create only one solution. Thus, (D) is correct. For the record, (A) has two points of intersection and (C) has none.