PSAT Math Multiple-Choice Question 349: Answer and Explanation

Question: 349

What is the value of |a - b| if a and b are constants and the above system of equations has no solution?

• A. -13
• B. -8
• C. 8
• D. 13

Correct Answer: D

Explanation:

D

Difficulty: Hard

Category: Number of Possible Solutions

Getting to the Answer: Rearrange the equations and write them on top of each other so that the x- and y-terms line up:

In a system of equations that has no solution, the x--coefficients must equal each other and the y-coefficients must equal each other, but the constant on the right needs to be different. Thus, for the x-coefficients, 36 = 6b and b = 6. For the y-coefficients, a = -7. The question asks for the value of |a - b|, which is |-7 - 6| = |-13| = 13, choice (D).