\(\dfrac{4^x}{2^{x+y}}=8\Rightarrow2^{2x}=2^3.2^{x+y}\Rightarrow2^{2x}=2^{x+y+3}\Rightarrow2x=x+y+3\Rightarrow x-y=3\left(1\right)\)
\(\dfrac{9^{x-y}}{3^{5y}}=243\Rightarrow3^{2\left(x-y\right)}=3^5.3^{5y}\Rightarrow3^{2\left(x-y\right)}=3^{5y+5}\Rightarrow2\left(x-y\right)=5y+5\Rightarrow2x-7y=5\left(2\right)\)
\(\left(1\right)\Rightarrow2x-2y=6\left(3\right)\)
\(\left(3\right)-\left(2\right)\Rightarrow5y=11\Rightarrow y=\dfrac{11}{5}\notin N\)
Vậy không tồn tại \(x;y\in N\)