Determine if $(3,-6,7)$ is a solution of the system. \[ \begin{array}{c} x+y+z=4 \\ x-2 y-z=8 \\ 2 x-y-2 z=-2 \end{array} \] Choose the correct answer below. The ordered triple is not a solution to the system. The ordered triple is a solution to the system.

Step 1 ：Substitute the values of the ordered triple $(3,-6,7)$ into the system of equations.

Step 2 ：For the first equation, we have $3 + (-6) + 7 = 4$, which is true.

Step 3 ：For the second equation, we have $3 - 2*(-6) - 7 = 8$, which is also true.

Step 4 ：For the third equation, we have $2*3 - (-6) - 2*7 = -2$, which is true.

Step 5 ：Since the left-hand side equals the right-hand side for all three equations, the ordered triple is a solution to the system.

Step 6 ：Final Answer: The ordered triple $(3,-6,7)$ is a \(\boxed{\text{solution to the system}}\).