Answer
$(\sqrt 2,\sqrt 2),(-\sqrt 2,-\sqrt 2)$
Work Step by Step
$x^{2}+4y^{2}=10$ Equation $(1)$
$y=x$ Equation $(2)$
Substituting $y = x $ in Equation $(1)$
$x^{2}+4y^{2}=10$
$x^{2}+4x^{2}=10$
$5x^{2}=10$
$x^{2}=2$
$x = ±\sqrt 2$
$x = \sqrt 2$ or $x = -\sqrt 2$
From Equation $(2)$
$y = ±\sqrt 2$
$y = \sqrt 2$ or $y = -\sqrt 2$
Solutions $(\sqrt 2,\sqrt 2)$ and $(-\sqrt 2,-\sqrt 2)$ both satisfies the equations $(1)$ and $(2)$.
So, solutions are $(\sqrt 2,\sqrt 2)$ and $(-\sqrt 2,-\sqrt 2)$
