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.

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