Use Gaussian elimination to find the complete solution to the system of equations, or show that none exists.
\[
\left\{\begin{array}{rr}
6 x+3 y+4 z= & -35 \\
2 x-6 y-4 z= & -6 \\
x+y-z= & 4
\end{array}\right.
\]

Step 1 ：Given the system of equations: \[\left\{\begin{array}{rr} 6 x+3 y+4 z= & -35 \\ 2 x-6 y-4 z= & -6 \\ x+y-z= & 4 \end{array}\right.\]

Step 2 ：We use the Gaussian elimination method to solve this system. The steps involved in Gaussian elimination method are: 1. Swap the rows if necessary to bring a row with a non-zero leading coefficient to the top. 2. Multiply each side of the equation by a non-zero constant to make the leading coefficient 1. 3. Add or subtract multiples of the top row from the other rows to make the coefficients below the leading 1 equal to zero. 4. Repeat the process for the remaining rows.

Step 3 ：After performing Gaussian elimination, we get the following system of equations: \[\begin{bmatrix} 6 & 3 & 4 \\ 0 & -7 & -5 \\ 0 & 0 & -1 \end{bmatrix}\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -14 \\ -40 \\ 9 \end{bmatrix}\]

Step 4 ：Solving this system, we find the solution to be \(x = -2\), \(y = 5\), and \(z = -9\).

Step 5 ：Final Answer: The solution to the system of equations is \(\boxed{x = -2, y = 5, z = -9}\).