$2^{x}$ = $2^{(14-4y)}$
$3^{(5x-13y)}$ = $3^{4}$
You asked:
Solve the system of equations:\[\begin{aligned}{2}^{x} &= {2}^{14 - 4 y}\\{3}^{5 x - 13 y} &= {3}^{4}\end{aligned}\]
MathBot Answer:
The system of equations has \(2\) solutions.
\[x = \frac{\log{\left(205891132094649 \right)}}{5 \log{\left(3 \right)}}, y = 2\]\[x = \frac{\log{\left(81 \cdot 3^{\frac{65 \log{\left(2^{\frac{2}{5}} \right)}}{\log{\left(2 \right)}}} \right)}}{5 \log{\left(3 \right)}}, y = \frac{5 \log{\left(2^{\frac{2}{5}} \right)}}{\log{\left(2 \right)}}\]