Simultaneous equations involving indices

Question

Please can someone help me solve this. I saw it in a text but I have tried to solve all to no avail.

$$3^x + 9^{2y} = 27\\2^x + 4^{-y} = \frac18 $$

Find 2$x$ + 3$y$

Answer 1

\begin{align} 3^x + 9^{2y} &= 27\\ 3^{4y} &= 3^3 - 3^x \\ 3^{4y} &< 3^3 \\ y &< 0.75 \\ \hline 2^x + 4^{-y} &= \frac18 \\ 2^{-2y} &= 2^{-3} - 2^x \\ 2^{-2y} &< 2^{-3} \\ -2y &< -3 \\ y &> 1.5 \end{align}

Since we can't have both $y < 0.75$ and $y > 1.5$, there is no solution.