elimination part of a mathematical question During solving a math question I got stuck in the elimination part and I couldn't proceed! Can someone help me, please? 
$$2(x+y)-3^\frac 1{2}(x-y)=0$$
$$4(x+y)+2(3)^{\frac 1{2}}(x-y)+9z=1$$
$$x+y+z=0$$
I want to get the values for $x$, $y$, and $z$. 

I would like to change the variables here.
let:
$u = x+y\\
v = \frac {\sqrt 3}{2} (x-y)$
then
$2u-2v = 0\\
4u + 4v + 9z = 1\\
u+z = 0$
$u=-1, v = -1, z = 1$
Now back to $x,y$
$x+y = u\\
x-y = \frac {2}{\sqrt 3}v$
$x+y = -1\\
x-y = -\frac {2}{\sqrt 3}$
$2x = -1-\frac {2}{\sqrt 3}\\
2y = -1 + \frac {2}{\sqrt 3}\\
x = -\frac {1}{2} - \frac {\sqrt 3}{3}\\
y = -\frac {1}{2} + \frac {\sqrt 3}{3}\\
z = 1$
