The graph of a quadratic function and a linear function are shown. The parabola opens upwards and has its vertex at $(0,-3)$, passing through $(-1,-2)$ and $(2,1)$. The line passes through $(-1,-2)$ and $(2,1)$. How many distinct solutions $(x,y)$ does this system have?

(Assume a graph is provided showing the parabola $y=x^2-3$ and the line $y=x-1$ intersecting at $(-1,-2)$ and $(2,1)$.)