It might help if you realise from your equations that .
See what you can do with the latter three equations.
Well, why not just take the square root of both sides?x(x+ y+ z)= 2- yz
y(x+ y+ z)= 4- xz
x(x+ y+ z)= 8- yz
Find the value of |x+ y+ z|
But I'm stuck on