TeX source:

\left[\begin{array}{rrr|r}1 & -3 & -5 & -2 \\2 & -5 & -4 & 5 \\-3 & 5 & 4 & 6\end{array}\right] \rightarrow \begin{aligned}&x-3 y-5 z=-2 \\&2 x-5 y-4 z=5 \\&-3 x+5 y+4 z=6\end{aligned}