I would really appreciate help with this system of equations:
$ \left\{ \begin{array}{c} ax+by=c \\ cx+az=b \\ bz+cy=a \end{array} \right. $
Here $a, b$ and $c$ are given real numbers, such that $abc\neq 0$ and $x, y$ and $z$ are the unknowns.
I am kind of stuck with it and can't think of anything that I could do with it. I think that to solve it I should express $x, y$ and $z$ in terms of $a, b$ and $c$ but I can't figure out just how should I do it.