$\left\{\begin{array}{l}x-3 y+5 z=1 \\ x+2 y+y=12 \\ 2 x-y+3 z=10\end{array}\right.$

Step 1 ：\(\left\{\begin{array}{l}x-3 y+5 z=1 \\ x+2 y+y=12 \\ 2 x-y+3 z=10\end{array}\right.\)

Step 2 ：\(A = \begin{bmatrix} 1 & -3 & 5 \\ 1 & 3 & 1 \\ 2 & -1 & 3 \end{bmatrix}, B = \begin{bmatrix} 1 \\ 12 \\ 10 \end{bmatrix}\)

Step 3 ：\(solution = \begin{bmatrix} 5.54545455 \\ 2.04545455 \\ 0.31818182 \end{bmatrix}\)

Step 4 ：\(\boxed{x \approx 5.55, y \approx 2.05, z \approx 0.32}\)