Answer
$(-4,1),(-4,-1)$
Work Step by Step
$x=-y^{2}-3$ Equation $(1)$
$x=y^{2}-5$ Equation $(2)$
From Equation $(1)$ and Equation $(2)$
$-y^{2}-3=y^{2}-5$
$5-3=y^{2}+y^{2}$
$2=2y^{2}$
$y^{2}=1$
$y= ±1$
$y=1$ or $y=-1$
Substitute $y$ values in Equation $(2)$
Let $y= 1$
$x=y^{2}-5$
$x=1^{2}-5$
$x=1-5$
$x=-4$
Let $y= -1$
$x=y^{2}-5$
$x=(-1)^{2}-5$
$x=1-5$
$x=-4$
$(-4,1),(-4,-1)$ satisfy given equations.
$(-4,1),(-4,-1)$ are the solutions.
