Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.
\[
\left\{\begin{array}{rr}
-x+y+z= & -1 \\
-x+4 y-8 z= & -22 \\
7 x-6 y-10 z= & 0
\end{array}\right.
\]

Step 1 ：Let's start with the given system of equations: \[\begin{cases} -x+y+z=-1 \\ -x+4y-8z=-22 \\ 7x-6y-10z=0 \end{cases}\]

Step 2 ：We use the Gaussian elimination method to solve this system. The first step is to form the augmented matrix of the system: \[\begin{bmatrix} -1 & 1 & 1 & -1 \\ -1 & 4 & -8 & -22 \\ 7 & -6 & -10 & 0 \end{bmatrix}\]

Step 3 ：Next, we perform row operations to bring the matrix to row-echelon form. After the operations, the matrix becomes: \[\begin{bmatrix} -1 & 1 & 1 & -1 \\ 0 & -3 & 9 & 21 \\ 0 & 0 & 0 & -9223372036854775808 \end{bmatrix}\]

Step 4 ：However, the last row of the matrix indicates that the system of equations is inconsistent and has no solution. This is because the last equation, \(7x - 6y - 10z = 0\), cannot be satisfied given the solutions to the first two equations.

Step 5 ：\(\boxed{\text{Final Answer: The given system of equations has no solution.}}\)