Solve the System of Equations $$\left\{ \begin{aligned}- x + y + 2 z & = 0 \\x + 2 y + z & = 6 \\- 2 x - y + z & = - 6\end{aligned} \right.$$

Multiple Choice

Solve the system of equations.
- $$\left\{ \begin{aligned}- x + y + 2 z & = 0 \\x + 2 y + z & = 6 \\- 2 x - y + z & = - 6\end{aligned} \right.$$

A) inconsistent (no solution)
B) $x = 2 - z$
$y = z + 2$
$z =$ any real number
C) $x = z + 2$
$y = 2 - z$
$z =$ any real number

D) $x = z + 2$
$y = z - 2$
$z =$ any real number