The graphs of a linear equation and a quadratic equation are shown. The line passes through $(-1,1)$ and $(2,4)$, and the parabola passes through $(-1,1)$, $(0,0)$, and $(2,4)$. What is the sum of the x-coordinates of all solutions $(x,y)$ to this system?

(Assume a graph is provided showing the line $y=x+2$ and the parabola $y=x^2$ intersecting at $(-1,1)$ and $(2,4)$.)