The graph of a system of an absolute value function, $y=|x-3|$, and a quadratic function, $y=(x-3{)}^2$, is shown. How many distinct solutions does this system of equations have?

(A graph showing the absolute value function $y=|x-3|$ and the parabola $y=(x-3{)}^2$ intersecting at $(2,1)$, $(3,0)$, and $(4,1)$ would be provided.)