Answer
$(1,3),(1,-3),(-1,3),(-1,-3)$
Work Step by Step
$x^{2}+y^{2}=10$ Equation $(1)$
$9x^{2}+y^{2}=18$ Equation $(2)$
Subtract Equation $(1)$ from Equation $(2)$
$9x^{2}+y^{2}-(x^{2}+y^{2})=18-10$
$9x^{2}+y^{2}-x^{2}-y^{2}=8$
$8x^{2}=8$
$x^{2}=1$
$x=±1$
$x=1$ or $x=-1$
Substitute $x$ values in Equation $(1)$ to get corresponding $y$ values.
Let $x=1$
$x^{2}+y^{2}=10$
$1^{2}+y^{2}=10$
$1+y^{2}=10$
$y^{2}=9$
$y=±3$
Let $x=-1$
$x^{2}+y^{2}=10$
$(-1)^{2}+y^{2}=10$
$1+y^{2}=10$
$y^{2}=9$
$y=±3$
$(1,3),(1,-3),(-1,3),(-1,-3)$ satisfy the given equations.
The solution set is $\{(1,3),(1,-3),(-1,3),(-1,-3)\}$
