PSAT Math Multiple-Choice Question 731: Answer and Explanation

Question: 731

Which of these equations, when combined into a set of equations with 4x = 2y - 6, will result in no solutions to the set?

• A. y = x - 4
• B. y = 2x + 10
• C. y = 4x - 1
• D.

Correct Answer: B

Explanation:

(B) Begin by determining the slope of the line in the given equation by putting it in slope-intercept form (y = mx + b):

4x = 2y - 6 → 2y = 4x + 6 → y = 2x + 3

The line portrayed in choice (B), y = 2x + 10, is the only option that has the same slope as the line in the problem. This means that the two lines will never intersect and will have no common solutions since they are parallel to one another. Be mindful that this will be true only as long as the y-intercepts of the lines are different. If the y-intercepts are the same, the lines will overlap, resulting in an infinite number of solutions.