Answer
0, 1, 2, 3, or 4 solutions
Work Step by Step
0 solutions: $x^2+y^2=1$ and $y=x^2-2$
1 solution: $x^2+y^2=1$ and $y=x^2+1$
2 solutions: $x^2+y^2=1$ and $y=x^2$
3 solutions: $x^2+y^2=1$ and $y=x^2-1$
4 solutions: $x^2+y^2=1$ and $y=x^2-3$