Systems of Polynomial Equations Practice Test

The curves $y=x^2-2x-3$ and $y=-x+1$ are graphed on the coordinate plane, and their intersection points are visible. How many solutions does the system have?

A parabola $y=x^2+4x+5$ models the cross-section of a bowl, and the line $y=1$ represents the water level. How many real solutions does the system have?