AMC 12A 2017 Problem 9

Let S be the set of points (x, y) in the coordinate plane such that two of the three quantities 3, x+2, and y-4 are equal and the third of the three quantities is no greater than this common value. Which of the following is a correct description of S ?

Answer Choices
A. a single point
B. two intersecting lines
C. three lines whose pairwise intersections are three distinct points
D. a triangle
E. three rays with a common endpoint