Solve the System of Equations $$\left\{ \begin{aligned}x - y + 4 z & = 2 \\5 x + z & = 0 \\x + 2 y + z & = - 4\end{aligned} \right.$$

Multiple Choice

Solve the system of equations.
- $$\left\{ \begin{aligned}x - y + 4 z & = 2 \\5 x + z & = 0 \\x + 2 y + z & = - 4\end{aligned} \right.$$

A) $x = 0 , y = 0 , z = - 2$
B) Inconsistent, $\varnothing$
C) $x = 0 , y = - 2 , z = 2$
D) $x = 0 , y = - 2 , z = 0$