In the $xy$-plane, the graph of the equation $y=5x-4$ intersects the graph of the equation $y=x^2$ at two points. What is the sum of the $x$-coordinates of the two points?

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We are given a system of equations. We can use substitution to find the $x$-coordinates of the points of intersection.

$$y=5x-4$$ $$y=x^2$$ $$x^2=5x-4$$ $$x^2-5x+4=0$$

We can solve this quadratic using any method. Review Quadratic Equations for a review of solving quadratics. Below we show factoring.

$$=(x-4)(x-1)$$ $$x=4 \text{ and } 1$$ $$4 + 1 = \boxed{5 }$$