\(\left(\frac{3}{4}\right)^{x}\left(\frac{2}{3}\right)^{y}=\frac{32}{27}\)xpressing in another form, we have
\(\left(3^{\prime} \cdot 4^{-1} x\right)\left(2 \cdot 3^{-1}\right)=2^{5} \cdot 3^{-3}\)
\(=(3 \cdot 2 \cdot 21) \cdot\left(2^{1} \cdot 3^{-1}\right)=2^{5} \cdot 3^{-}\)
We add the power of equal base. we have \(2^{-2}+3.3^{\prime}:=2^{5} \cdot 3^{-3}\)
equating powers of equal base, we have \(\Rightarrow-2 x+y=5 \ldots(1)\)
\(+x-y=-3 \ldots \ldots+(1)\)
\(x=-2 \cdot y=x+3=-2+3=1\)
So that
3 y-2 x=3(1)-2(-2)=3+4=7