Question

Решить систему уравнений

Answer 1

$left{begin{array}{l} 5^{x+1}cdot3^y=75 \ 3^xcdot5^{y-1}=3 end{array}$
$left{begin{array}{l} 5cdot 5^xcdot3^y=75 \ 3^xcdot frac{1}{5} cdot 5^y=3 end{array}$
$left{begin{array}{l} 5^xcdot3^y=15 \ 3^xcdot 5^y=15 end{array}$
$dfrac{5^xcdot3^y}{3^xcdot5^y} = dfrac{15}{15}$
$left( dfrac{5}{3} right)^xcdot left( dfrac{3}{5} right)^y=1 \\ left( dfrac{5}{3} right)^xcdot left( dfrac{5}{3} right)^{-y}=1 \\ left( dfrac{5}{3} right)^{x-y}=left( dfrac{5}{3} right)^0 \\ x-y=0 \ Rightarrow x=y \ 5^xcdot3^x=15 \ (5cdot3)^x=15 \ 15^x=15^1 \ Rightarrow x=1 \ Rig$
Ответ: (1; 1)

Answer 2

спасибо