Q:

Simultaneous Equation Problem

$$x + 2y + z = 5(x + y)(y + z)\\
x + y + 2z = 7(y + z)(z + x)\\
2x + y + z = 6(z + x)(x + y).$$
Find the value of $24^3xyz$.
This seems a problem concerning simultaneous equations. I didn't even know where to start! Please Help!
** EDIT** 
Can the OP confirm that it is $24^3 xyz$ and not $24^{3xyz}$? I am asking here to make it easier for OP to answer without using LaTeX.

A:

Hint:Assume $x+y = a ,y+z = b, z+x = c$ and express both LHS and RHS of all 3 equations in terms of $a,b,c$. After some simplification, you should be able to get a system of linear equations in $\frac{1}{a},\frac{1}{b},\frac{1}{c}$.
Can you solve it now?

