I want to know how to express $a$ in terms of $x$, $y$ and $z$ in the following system (i.e., I want to find the function $a(x,y,z)$). And how to investigate (and to play with the equations) to know whether a variable can expressed in terms of $x, y, z$ or not in similar situations?
$\begin{cases} x + 2y -z = 2\\ 2x + 5y -(a+2)z = 3\\ -x + (a+5)y + z = 1 \end{cases}$
P.S.: I would enjoy the solutions written in Maple or Mathematica format too.