PSAT Math Multiple-Choice Question 343: Answer and Explanation

Question: 343

For which of the following values of w will the system of equations above have no solution?

• A. -8
• B. -4
• C. 4
• D. 8

Correct Answer: A

Explanation:

A

Difficulty: Hard

Getting to the Answer: One way to answer the question is to think about the graphs of the equations. Graphically, a system of linear equations that has no solution indicates two parallel lines or, in other words, two lines that have the same slope. Write each of the equations in slope-intercept form, y = mx + b, and set their slopes, m, equal to each other to solve for w.

First equation:

Second equation:

Set the slopes equal:

This matches (A). Alternatively, you could manipulate the first equation to make the x-coefficients the same and then equate the coefficients of y to solve for w.