PSAT Math Multiple-Choice Question 768: Answer and Explanation

Question: 768

At what point in the xy-plane will the functions y = 4x – 3 and y = –x + 2 intersect?

• A.
• B.
• C.
• D.

Correct Answer: C

Explanation:

(C) Notice that both functions give equations of lines. To find the point of intersection, we want to find the point (x, y) that is on both lines. Since (x, y) is on both lines, we can find this common x-value by setting the right sides of both equations equal to one another:

Combine like terms by adding to both sides and by adding 3 to both sides:

Solve for x by dividing both sides by (in other words, multiply both sides by ):

This is enough to narrow it down to choice (C), but you could solve for y by plugging in
for x in either equation: