Answer
$(-\sqrt{6},6)$
Work Step by Step
Step 1. Rewrite the equations.
$x=-\sqrt{y}$
$y^2-4x^2-12=0$
Step 2. Substitute the first equation to the second one and then solve for $y$.
$y^2-4(-\sqrt{y})^2-12=0$
$y^2-4y-12=0$
$(y+2)(y-6)=0$
$y=-2$ and $y=6$
Step 3. Solve for $x$.
For $y=-2$, $x=-\sqrt{-2}$ (imaginary solution)
For $y=6$, $x=-\sqrt{6}$ (real solution)
Step 4. Conclude the solution.
The solution is $(-\sqrt{6},6)$.
