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