Determine if $(3,-6,2)$ is a solution of the system.
\[
\begin{aligned}
x+y+z & =-1 \\
x-2 y-z & =13 \\
2 x-y-2 z & =8
\end{aligned}
\]
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
\(\boxed{\text{The ordered triple is a solution to the system.}}\)
Step 1 ：Substitute the values of the ordered triple $(3,-6,2)$ into the system of equations.
Step 2 ：For the first equation, we have $3 + (-6) + 2 = -1$, which is true.
Step 3 ：For the second equation, we have $3 - 2*(-6) - 2 = 13$, which is also true.
Step 4 ：For the third equation, we have $2*3 - (-6) - 2*2 = 8$, which is true as well.
Step 5 ：Since all three equations are true when we substitute the values of the ordered triple $(3,-6,2)$, this means that the ordered triple is a solution to the system.
Step 6 ：\(\boxed{\text{The ordered triple is a solution to the system.}}\)
