Solve the system. \[ \begin{array}{l} 2 x+6 y-z=6 \\ 3 x-3 y+5 z=-5 \\ 7 x+9 y-2 z=12 \end{array} \]

Step 1 ：We are given the system of equations: \[\begin{array}{l} 2x+6y-z=6 \ 3x-3y+5z=-5 \ 7x+9y-2z=12 \end{array}\]

Step 2 ：We can represent this system in matrix form as A*x = b, where A is the matrix of coefficients, x is the column vector of variables, and b is the column vector of constants.

Step 3 ：Matrix A is \[\begin{bmatrix} 2 & 6 & -1 \ 3 & -3 & 5 \ 7 & 9 & -2 \end{bmatrix}\] and vector b is \[\begin{bmatrix} 6 \ -5 \ 12 \end{bmatrix}\].

Step 4 ：We solve for x by finding the inverse of A and multiplying it with b. The solution vector x is \[\begin{bmatrix} 0.625 \ 0.625 \ -1 \end{bmatrix}\].

Step 5 ：So, the solution to the system of equations is \(x = 0.625\), \(y = 0.625\), and \(z = -1\).

Step 6 ：Final Answer: The solution to the system of equations is \(\boxed{x = 0.625, y = 0.625, z = -1}\).