Given 2x = 8y+1 and 9y = 3x-9 , then value of x + y is = ?

Answer: Option D

$$\begin{array}{rl}& {\text{2}}^x\text{ = }{\text{8}}^{y+1}\\ & \iff {\text{2}}^x\text{ = }{\left(2^3\right)}^{y+1}=2^{\left(3y+3\right)}\\ & \iff x=3y+3\\ & \iff x-3y=\mathrm{3.......}(i)\\ & 9^y=3^{x-9}\\ & \iff {\left(3^2\right)}^y\text{ = }{\text{3}}^{x-9}\\ & \iff 2y=x-9\\ & \iff x-2y=\mathrm{9......}(\text{ii})\\ & \text{Subtracting (i) from (ii),}\\ & \text{we}\text{get}y=6\\ & \text{Putting }y\text{ = 6 in (i),}\\ & \text{we get }x\text{ = 21}\\ & \therefore x+y=21+6=27\end{array}$$