Given the following system of equations:

\[
\begin{aligned}
& 3 y+2 x=z+1, \\
& 3 x+2 z=8-5 y, \\
& 3 z-1=x-2 y
\end{aligned}
\]

solve for \(x, y\), and \(z\) using the following methods:

(a) Inverse method;

(b) Cramer's rule;

(c) Gauss elimination;

(d) Maple software package.