$2^{x}$ = $4^{(7-2y)}$
$3^{(5x-13y)}$ =81
You asked:
Solve the system of equations:\[\begin{aligned}{2}^{x} &= {4}^{7 - 2 y}\\{3}^{5 x - 13 y} &= 81\end{aligned}\]
MathBot Answer:
The system of equations has \(2\) solutions.
\[x = \frac{\log{\left(205891132094649 \right)}}{5 \log{\left(3 \right)}}, y = 2\]\[x = \frac{\log{\left(81 \cdot 3^{\frac{65 \log{\left(8192 \cdot \sqrt[5]{2} \right)}}{33 \log{\left(2 \right)}}} \right)}}{5 \log{\left(3 \right)}}, y = \frac{5 \log{\left(8192 \cdot \sqrt[5]{2} \right)}}{33 \log{\left(2 \right)}}\]