\(2^x=4^{y-1}\Rightarrow2^x=2^{2y+2}\Rightarrow x=2y+2\\ 27^y=3^{x+8}\Rightarrow3^{3y}=3^{x+8}\Rightarrow2y=x+8\\ \Rightarrow\left\{{}\begin{matrix}x=2y+2\\x+8=2y\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=x+8+2\\x+8=2y\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=5\\y=\dfrac{13}{2}\end{matrix}\right.\)