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