a) Ta có: \(2^{x-1}\cdot3^{y+1}=12^{x+y}\)
\(\Leftrightarrow2^{x-1}\cdot3^{y+1}=4^{x+y}\cdot3^{x+y}\)
\(\Leftrightarrow2^{x-1}\cdot3^{y+1}=2^{2x+2y}\cdot3^{x+y}\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-1=2x+2y\\y+1=x+y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}1-1=2\cdot1+2y\\x=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2+2y=0\\x=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2y=-2\\x=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-1\\x=1\end{matrix}\right.\)
