Answer
$(1,1)(-1,-1)$
Work Step by Step
$x^{2}+4y^{2}=5$ Equation $(1)$
$y=x$ Equation $(2)$
Substitute $y=x$ in Equation $(1)$
$x^{2}+4y^{2}=5$
$x^{2}+4x^{2}=5$
$5x^{2}=5$
$x^{2}=1$
$x=±1$
$x=1$ or $x=-1$
Substitute $x$ values in Equation $(2)$ to get corresponding $y$ values.
Let $x=1$
$y=x$
$y=1$
Let $x=-1$
$y=x$
$y=-1$
Both $(1,1)(-1,-1)$ satisfy the given equations.
Solutions are $(1,1)(-1,-1)$
