Answer
$(-\sqrt6, 6)$
Work Step by Step
Given the system of equations:
1. $x + \sqrt y = 0$
2. $y^2 - 4x^2 = 12$
It asks to find all solutions.
Substitute $x = -\sqrt y$
$y^2 - -4(-\sqrt y)^2= 12$
$y^2 - 4y - 12 = 0$
$(y - 6) (y + 2) = 0$
y = 6, -2
Substitute the values into the equation
$x + \sqrt 6 = 0$
$x = -\sqrt 6$
$x + \sqrt -2 = 0$
Not possible
All solutions:
$(-\sqrt6, 6)$
