$\displaystyle x(x+y+z)=2-yz$

$\displaystyle y(x+y+z)=4-xz$

$\displaystyle z(x+y+z)=8-yx$

Find the value of $\displaystyle |x+y+z|$

I know $\displaystyle \sqrt{(x+y+z)^2}=|x+y+z|$

But I'm stuck on $\displaystyle (x+y+z)^2=14-(xy+yz+xz)$

Any tips?