Answer
$(\sqrt 6,\sqrt 5),(\sqrt 6,-\sqrt 5),(-\sqrt 6,\sqrt 5),(-\sqrt 6,-\sqrt 5)$
Work Step by Step
We use the elimination method to solve this system. To eliminate $X^2$ when we add the two equations, we multiply both sides of the second equation by -1. Then
$(-1)(x^2-y^2)=(-1)(1)$
$-x^2+y^2=-1$
Add the above equation to the first equation,
$4y^2=20$
$y^2=5$
$y=+/-\sqrt 5$
Let $y=\sqrt 5$ and $y=-\sqrt 5$ in either original equation. We choose the second equation.
Let $y=\sqrt 5$,
$x^2-(\sqrt 5)^2=1$
$x=+/-\sqrt 6$
Let $y=-\sqrt 5$,
$x^2-(-\sqrt 5)^2=1$
$x=+/-\sqrt 6$
The solution set is $(\sqrt 6,\sqrt 5),(\sqrt 6,-\sqrt 5),(-\sqrt 6,\sqrt 5),(-\sqrt 6,-\sqrt 5)$
