# 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 $24^3xyz$.

** 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.
• @user44197 I'd bet the house that the OP wants $24^3 xyz$. Jan 5 '14 at 7:55
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 $\frac{1}{a},\frac{1}{b},\frac{1}{c}$.