PSAT Math Multiple-Choice Question 348: Answer and Explanation

Question: 348

If k is a constant and the above system of linear equations has infinitely many solutions, what is the value of k?

• A. -8
• B. -4
• C. -2
• D. -1

Correct Answer: C

Explanation:

C

Difficulty: Hard

Category: Number of Possible Solutions

Getting to the Answer: The system has infinitely many solutions, so both equations must describe the same line. Notice that if you multiply the x- and y-coefficients in the second equation by 16, you arrive at the x- and y-coefficients in the first equation. The constant k times 16 must then equal the constant in the first equation, or -32:

Therefore, (C) is correct.