Answer
See below
Work Step by Step
$\begin{bmatrix}
2 & -1 & -4|5\\3&2&-5|8 \\5&6&-6|20\\1&1&-3|-3
\end{bmatrix}\approx \begin{bmatrix}
5&6&-6|20\\3&2&-5|8\\2 & -1 & -4|5\\1&1&-3|-3
\end{bmatrix}\approx \begin{bmatrix}
5&6&-6|20\\ 0& \frac{-8}{5}&-\frac{7}{5}|-4 \\0 & -\frac{17}{5} &\frac{-8}{5}| -3\\ 0&-\frac{1}{5}&\frac{-9}{5}| -7
\end{bmatrix} \approx \begin{bmatrix}
5&6&-6|20\\ 0 & -\frac{17}{5} &\frac{-8}{5}| -3\\0& \frac{-8}{5}&-\frac{7}{5}|-4\\ 0&-\frac{1}{5}&\frac{-9}{5}| -7
\end{bmatrix}\approx\begin{bmatrix}
5&6&-6|20\\ 0 & -\frac{17}{5} &\frac{-8}{5}| -3\\0 & 0&\frac{-11}{17}| -\frac{44}{17}\\ 0& 0 & -\frac{29}{17}|-\frac{116}{17}
\end{bmatrix}\approx \begin{bmatrix}
5&6&-6|20\\ 0 & -\frac{17}{5} &\frac{-8}{5}| -3\\ 0& 0 & -\frac{29}{17}|-\frac{116}{17}\\0 & 0&\frac{-11}{17}| -\frac{44}{17}
\end{bmatrix}\approx\begin{bmatrix}
5&6&-6|20\\ 0 & -\frac{17}{5} &\frac{-8}{5}| -3\\ 0& 0 & -\frac{29}{17}|-\frac{116}{17}\\0 & 0&0| 0
\end{bmatrix}$
$1.P_{13}\\
2.A_{12}(-\frac{3}{5}),A_{13}(-\frac{2}{5}),A_{14}(-\frac{1}{5})\\
3.P_{23}\\
4.A_{23}(-\frac{8}{17}),A_{24}(\frac{-1}{17})\\
5.P_{34}\\
6.A_{34}(\frac{-11}{29})$
The unique solution $(10,-1,4)$
