Answer
$\left\{\begin{array}{llll}
x & & +4z & =4\\
& y & +3z & =2\\
& & 0 & =0
\end{array}\right.$
Consistent.
Solution set = $\{(x,y,z)\ |\ x=-4z+4,\ \ y=-3z+2,\ \ z\in \mathbb{R}\}$
Work Step by Step
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
x & & +4z & =4\\
& y & +3z & =2\\
& & 0 & =0
\end{array}\right.$
The third equation is always satisfied. The system is consistent.
Take $z\in \mathbb{R}$,
Equation 2 $\Rightarrow y=-3z+2$
Equation 1 $\Rightarrow x=-4z+4$
Solution set = $\{(x,y,z)\ |\ x=-4z+4,\ \ y=-3z+2,\ \ z\in \mathbb{R}\}$
