# Math Help - Simultaneous Equations

1. ## Simultaneous Equations

$x(x+y+z)=2-yz$
$y(x+y+z)=4-xz$
$z(x+y+z)=8-yx$

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

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

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

Any tips?

2. ## Re: Simultaneous Equations

It might help if you realise from your equations that $\displaystyle x + y + z = \frac{2 - yz}{x} = \frac{4 - xz}{y} = \frac{8 - yx}{z}$.

See what you can do with the latter three equations.

3. ## Re: Simultaneous Equations

Have tried cross multiplying them, nothing works out right now.
Any other options?

4. ## Re: Simultaneous Equations

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|

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

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

Any tips?
Well, why not just take the square root of both sides?
$|x+ y+ z|= \sqrt{14- (xy+ xz+ yz)}$