The boundary lines of y ≥ 2x - 4 and y ≤ -x + k intersect at the point where x = 2. What is the value of k?

The boundary lines are $y = 2x - 4$ and $y = -x + k$, and they meet where $x = 2$. On the first line, $y = 2(2) - 4 = 0$. So the intersection point is $(2, 0)$. This point must also lie on the second line: $0 = -2 + k$, which gives $k = 2$. Check: the second line becomes $y = -x + 2$, and at $x = 2$ it gives $y = 0$. A common wrong answer is $-2$, which comes from a sign error when solving $0 = -2 + k$. Another is 4, from using the intercept of the first line, and a third is 0, the $y$-value of the intersection.