Question

$1. left { {{x+2y=3} atop {3^{x-y} =81}} right. 2. left { {{4^{x} *2 ^{y}=32 } atop {3^{8x+1} =3^{3y} }} right. 3. left { {{3^{3x-2y}=81 } atop {3^{6x} *3^{y} }=27} right.$

Answer 1

1) $left { {{x=3-2y} atop {3^{x-y} =81}} right.$
$left { {{x=3-2y} atop {3^{3-2y-y} =81}} right.$
$left { {{x=3-2y} atop {3^{3-3y}=3^{4}}} right.$
$3-3y=4$
$-3y=4-3$
$y=- frac{1}{3}$
$x=3-2y=3- frac{2}{3}=frac{7}{3}=2frac{1}{3}$

Ответ: $(2frac{1}{3};-frac{1}{3})$

2) $left { {{2^{2x+y}=2^{5}} atop {8x+1=3y}} right.$
$left { {{2x+y=5} atop {8x+1=3y}} right.$
$left { {{y=5-2x} atop {8x+1=3(5-2x)}} right.$
$8x+1=15-6x$
$14x=14$
$x=1$
$y=5-2x=5-2=3$

Ответ: (1; 3)

3) $left { {{3^{3x-2y}=3^{4}} atop {3^{6x+y}=3^{3}} right.$
$left { {{3x-2y=4} atop {6x+y=3} right.$
$left { {{3x-2(3-6x)=4} atop {y=3-6x} right.$
$3x-6+12x=4$
$15x=10$
$x= frac{2}{3}$
$y=3-6x=3-frac{2*6}{3}=3-4=-1$

Ответ: $(frac{2}{3};-1)$