Answer
See below
Work Step by Step
$\begin{bmatrix}
1 & 2 &1|1\\
3 &5 &1|3\\
2& 6&7|1
\end{bmatrix}\approx \begin{bmatrix}
3 &5 &1|3\\
1&2 &1|y_2-2y_1\\
2 & 6& 7|1
\end{bmatrix} \approx \begin{bmatrix}
3 & 5 &1|3\\
0 & \frac{1}{3} & \frac{2}{3}| 0\\
0 & \frac{8}{3}& \frac{19}{3}|-1
\end{bmatrix} \approx \approx \begin{bmatrix}
3 & 5 &1|3\\
0 & \frac{8}{3}& \frac{19}{3}|-1\\
0 & 0 & \frac{-1}{8}| \frac{1}{8}
\end{bmatrix}$
$1.P_{12}\\
2.A_{12}(-\frac{1}{3}),A_{13}(-\frac{2}{3})\\
3.P_{23}\\
4.A_{23}(-\frac{1}{8})$
The unique solution $(-2,2,-1)$
