2019 AMC 8

First, we need to find the coordinates where the graphs intersect.

We want the points x and y to be the same. Thus, we set and get Plugging this into the equation, , and intersect at , we call this line x.

Doing the same thing, we get Thus, . Also, and intersect at , and we call this line y.

It's apparent the only solution to is Thus, and intersect at , we call this line z.

Using the Shoelace Theorem we get:

So, our answer is

We might also see that the lines and are mirror images of each other. This is because, when rewritten, their slopes can be multiplied by to get the other. As the base is horizontal, this is an isosceles triangle with base 8, as the intersection points have a distance of 8. The height is so