Answer
$\left\{\begin{array}{llll}
x & & +2z & =-1\\
& y & -4z & =-2\\
& & 0 & =0
\end{array}\right.$
Consistent,
Solution set = $\{(x,y,z)\ |\ x=-1-2z,\ \ y=-2+4z,\ \ z\in \mathbb{R}\}$
Work Step by Step
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
x & & +2z & =-1\\
& y & -4z & =-2\\
& & 0 & =0
\end{array}\right.$
The third equation is always satisfied. The system is consistent.
Take $z\in \mathbb{R}$,
Equation 2 $\Rightarrow y=4z-2$
Equation 1 $\Rightarrow x=-2z-1$
Solution set = $\{(x,y,z)\ |\ x=-1-2z,\ \ y=-2+4z,\ \ z\in \mathbb{R}\}$
