53Intersecting lines, find k

In the xy-plane, the lines y = 2x + 7 and y = −x + k intersect at a point whose x-coordinate is 3. What is the value of the constant k?

The value of k is 16. Since both lines pass through the same point at x = 3, the first line gives y = 2(3)+7 = 13, and plugging x=3, y=13 into y = −x + k gives 13 = −3 + k, so k = 16.