<s>[INST] Solution of System of linear equations I have three equations:
$$
\begin{cases}
4y + z = 2\\
2x + 6y - 2z = 3\\
4x + 8y - 5z = 4
\end{cases}
$$
Applying Gauss elimination I get:
$$ \left[
    \begin{array}{ccc|c}
      1&0&-\frac{7}{4} & 0\\
      0 & 1 & \frac{1}{4}  & \frac{1}{2} \\
      0 & 0 & 0 & 0
    \end{array}
\right] $$
Now how can I get the solution as there one row is eliminated leaving 2 equations with 3 unknowns?
 [/INST] You can arbitrarily choose $z$. Then, $x$ and $y$ can be computed from that:
$$
x - \frac{7}{4}z = 0 \;\Rightarrow\; x = \frac{7}{4} z\\
y + \frac{1}{4}z = \frac{1}{2} \;\Rightarrow\; y=\frac{1}{2} - \frac{1}{4}z
$$  
</s>