### Instruction: Find $2^x$ if

\begin{align*}
2^x+3^y&=5,\\
2^{x+2}+3^{y+1} &=18.
\end{align*}.### Response: This is a system of two exponential equations with two unknowns, $x$ and $y$.
I want to isolate $2^x$ and find its value, so I need to eliminate $y$ somehow.
I notice that the second equation can be rewritten as $4\cdot 2^x+3\cdot 3^y=18$.
This suggests that I can multiply the first equation by $3$ and subtract it from the second equation to eliminate $3^y$.
If I do that, I get $4\cdot 2^x-3\cdot 2^x=18-15$, which simplifies to $2^x=3$.