PSAT Math Multiple-Choice Question 167: Answer and Explanation

Question: 167

The equations of two lines are shown above. If the lines are graphed on the xy-plane, which of the following ordered pairs represents the point of intersection of the two lines?

• A. (8, 2)
• B. (16, 4)
• C. (24, 6)
• D. (32, 8)

Correct Answer: A

Explanation:

A

The question asks for the point of intersection, which is the point that satisfies both equations. There are specific points in the answers, so plug in the answers. Test the ordered pairs in both equations from the question and look for a pair that makes both equations true. Start with the simpler equation. Plug in each choice into the second equation. For (A), (8) = 2, so keep (A). For (B), (16) = 4, so keep (B). For (C), (24) = 6, so keep (C). For (D), (32) = 8, so keep (D). Since all four choices are solutions to the second equation, plug them into the first equation. For (A), the equation becomes 10(8) - 62 = 9(2). This simplifies to 80 - 62 = 18 or 18 = 18. This is true, so keep (A). Since the coordinates in (A) work in both equations, (A) must contain the intersection of the two lines. The correct answer is (A).