what is x + y?

Turn exponential equations into linear equations: $8^x=(2^3)^{x}=2^{3x}$ $2^{3x}=2^{y+2}$ $3x=y+2$ Now with the second equation: $16^{3x-y}=(4^2)^{3x-y}=4^{6x-2y}$ $4^{6x-2y}=4^y$ $6x-2y=y$ $6x=3y$ $2x=y$ With our two final equations, $3x=y+2$ and $2x=y$ , use substitution to solve: $3x=2x+2$ $x=2$ Plugging x back into the equation, we get: $y=4$ Therefore: $x+y=\boxed{6}$