Answer
$(-1, -1)$, $(1,1)$
Work Step by Step
$x^2+4y^2=5$
$y=x$
$x^2+4y^2=5$
$x^2+4(x)^2=5$
$x^2+4x^2=5$
$5x^2=5$
$5x^2/5=5/5$
$x^2=1$
$\sqrt {x^2} = \sqrt 1$
$x=±1$
$x=1$
$y=x$
$y=1$
$x=-1$
$y=x$
$y=-1$
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