Answer
$(-7,-20),(2,\frac{5}{2})$
Work Step by Step
$x^{2}+2y=9$ Equation $(1)$
$5x-2y=5$ Equation $(2)$
Add Equation $(1)$ and Equation $(2)$
$x^{2}+2y+5x-2y=9+5$
$x^{2}+5x=14$
$x^{2}+5x-14=0$
By factoring,
$(x+7)(x-2)=0$
$x=-7$ or $x=2$
Substitute $x$ values in Equation $(2)$ to get corresponding $y$ values.
Let $x=-7$
$5x-2y=5$
$5(-7)-2y=5$
$-35-2y=5$
$-2y=5+35$
$-2y=40$
$y=-20$
Let $x=2$
$5x-2y=5$
$5(2)-2y=5$
$10-2y=5$
$-2y=5-10$
$-2y=-5$
$y=\frac{5}{2}$
$(-7,-20),(2,\frac{5}{2})$ satisfy the given equations.
