\(\left\{{}\begin{matrix}x+2y=3\\4x+5y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4x+8y=12\\4x+5y=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3y=6\\x+2y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2\\x=-1\end{matrix}\right.\)
\(\Leftrightarrow4\left(x+2y\right)-\left(4x+5y\right)=4\cdot3-6\\ \Leftrightarrow4x+8y-4x-5y=6\\ \Leftrightarrow3y=6\\ \Leftrightarrow y=2\\ \Rightarrow x+2\cdot2=3\\ \Leftrightarrow x=-1\)