UNSW School Mathematics Competition Problems 1970

Solve for $x,y$ and $z$ the simultaneous system of equations
\begin{align*}
x(x+y) + z(x-y) & = a, \\
y(y+z) + x(y-z) & = b, \\
z(z+x) + y(z-x) & = c,
\end{align*}