Write the system of linear equations represented by the augmented matrix. (Use variables $x$, $y$, and $z$, if applicable.)
$\begin{bmatrix} 1 & 2 & -2 & : & 13 \\ 0 & 1 & 1 & : & 9 \\ 0 & 0 & 1 & : & -7 \end{bmatrix}$
Use back-substitution to solve the system.
$(x, y, z) = (\text{____})$