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