Question

Решить систему уравнений

Answer 1

ОДЗ :  x > 0   ;   y > 0

$\left\{\begin{array}{ccc}\log_{4}x-\log_{4}y=1 \\x-3y=16\end{array}\right \\\\\\\left\{\begin{array}{ccc}\log_{4}\dfrac{x}{y} =1\\x-3y=16\end{array}\right \\\\\\\left\{\begin{array}{ccc}\dfrac{x}{y} =4\\x-3y=16\end{array}\right \\\\\\\left\{\begin{array}{ccc}x=4y\\4y-3y=16\end{array}\right \\\\\\\left\{\begin{array}{ccc}x=4y\\y=16\end{array}\right\\\\\\\left\{\begin{array}{ccc}x=4\cdot16\\y=16\end{array}\right\\\\\\\left\{\begin{array}{ccc}x=64\\y=16\end{array}\right$

$Otvet:\boxed{(64 \ ; \ 16)}$