Answer
$\{\ (0,2),\ (0,-2),\ (-1,\sqrt{3}),\ (-1,-\sqrt{3})\ \}$
Work Step by Step
1. Eliminating:
Rewrite so the $y^{2}$ terms are lined up
Eliminate the $( y^{2})$ terms:
$\left\{\begin{array}{lll}
x-y^{2}=-4 & , & / \\
x^{2}+y^{2}=4 & , & / add
\end{array}\right.$
$x^{2}+x=0$
2. Solving:
$x^{2}+x=0$
$x(x+1)=0$
$x=0$ or $x+1=0$
3. Back-substituting into $x^{2}+y^{2}=4$:
$\left[\begin{array}{lll}
x=0 & or & x=1\\
0+y^{2}=4 & & 1+y^{2}=4 \\
y^{2}=4 & & y^{2}=3\\
y=\pm 2 & & y=\pm\sqrt{3}\\
& &
\end{array}\right]$
The solution set is
$\{\ (0,2),\ (0,-2),\ (-1,\sqrt{3}),\ (-1,-\sqrt{3})\ \}$
