\left[
\begin{array}{ccc}
1 & -2 & 3 \\
2 & -4 & 6
\end{array}
\right]
\sim
\left[
\begin{array}{ccc}
1 & -2 & 3 \\
0 & 0 & 0
\end{array}
\right]
\sim
\left[
\begin{array}{ccc}
1 & -2 & 3
\end{array}
\right] \Rightarrow \left x=3+2y