The graph shows a system of equations consisting of a linear equation and a quadratic equation. How many distinct solutions does this system have?

[Graph description: A coordinate plane with a parabola and a line. The parabola opens upwards with its vertex at the origin (representing $y=x^2$). The line passes through (0, 1) and (1, 2) (representing $y=x+1$). The line clearly intersects the parabola at two distinct points.]