Solving a system of non-linear equations

[Luke53]

Hello, I need help on this one, tried out about everything, but still no use, can't solve the following system:
y² - x y - 4x = 0
x² - x y + 4 y - 12 = 0
I can't isolate x or y in either of the two equations for substituting in the other.
So what's the trick to solve this?

Luke.

[nona.m.nona]

y² - x y - 4x = 0
x² - x y + 4 y - 12 = 0

One method might be to solve the first equation for Substitute the result into the second equation. Multiply through to clear the denominators, and expand.

Quite a few terms will drop out, leaving you with a quadratic which solves nicely with the Quadratic Formula.

[Luke53]

y² - x y - 4x = 0
x² - x y + 4 y - 12 = 0
x=y²/(y+4) (didn't see that I could factor x out in the first eqn.)
Substituting this in the second eqn and solving gives: 20y²-32y-192=0
y=4 and y= -12/5
subst. y=4 into the system gives x=2
Thanks.
Luke.