Answer
$(-2,-2)$, $(2,-2)$, $(-\sqrt 7,1)$, $(\sqrt 7,1)$
Work Step by Step
Re-arrange the given equations to get
$-x^2+y=-6$
$(-x^2+y)+(x^2+y^2)=-6+8$
$ \implies y^2+y-2=0$
This gives: $ (y+2)(y-1)=0$
when $ y=-2$ gives: $x^2=4 \implies x=2,-2$
when $ y=-1$ gives: $x^2=7 \implies x=-\sqrt 7, \sqrt 7$
Hence, our answers are: $(-2,-2)$, $(2,-2)$, $(-\sqrt 7,1)$, $(\sqrt 7,1)$
