Answer
$(0,-2)$, $(0,2)$, $(-1,-\sqrt 3)$, $(-1,\sqrt 3)$
Work Step by Step
Here, we have $-1(y^2-x)=(-1)(4) \implies x-y^2=-4$
Now, $(x-y^2) +(x^2+y^2) =-4+4$
This gives: $x^2+x=0 \implies x(x+1)=0$
when $x=0$ then we have $y^2-0=4 \implies y=-2$
and $y=2$
when $x=-1$ then we have $y^2-(-1)=4 \implies y^2=3$
and $y=\sqrt 3; -\sqrt 3$
Hence, our answers are: $(0,-2)$, $(0,2)$, $(-1,-\sqrt 3)$, $(-1,\sqrt 3)$
