Find the solution to the system of equations:
$$\{\begin{array}{l}x-2y+z=-1\\ y+2z=-3\\ x+y+3z=-6\end{array}$$
$$\begin{array}{l}x=\\ y=\\ z=\end{array}$$

Step 1 ：We are given a system of linear equations with three variables as follows:

Step 2 ：$$\{\begin{array}{l}x-2y+z=-1\\ y+2z=-3\\ x+y+3z=-6\end{array}$$

Step 3 ：We can solve this system using various methods such as substitution, elimination or matrix method. Here, we will use the matrix method.

Step 4 ：First, we represent the system of equations in matrix form. The matrix A represents the coefficients of the variables, and the matrix B represents the constants on the right side of the equations.

Step 5 ：A = $$\left[\begin{array}{ccc}1& -2& 1\\ 0& 1& 2\\ 1& 1& 3\end{array}\right]$$ and B = $$\left[\begin{array}{c}-1\\ -3\\ -6\end{array}\right]$$

Step 6 ：We then solve for the variables x, y, and z by finding the inverse of matrix A and multiplying it with matrix B.

Step 7 ：The solution is $$\left[\begin{array}{c}-2\\ -1\\ -1\end{array}\right]$$

Step 8 ：Thus, the solution to the system of equations is

Step 9 ：$$\begin{array}{l}x=\boxed{{\displaystyle -2}}\\ y=\boxed{{\displaystyle -1}}\\ z=\boxed{{\displaystyle -1}}\end{array}$$