Система lgx+lg2=lgy 3х-2у=-2

ОДЗ:

$left{begin{array}{l} x > 0 , y > 0 ; end{array}right$

$left{begin{array}{l} lg{x} + lg{2} = lg{y} , 3x - 2y = -2 ; end{array}right$

$left{begin{array}{l} lg{2x} = lg{y} , 3x - 2y = -2 ; end{array}right$

$left{begin{array}{l} 2x = y , 3x - 2y = -2 ; end{array}right$

$left{begin{array}{l} 2x = y , 3x - 2 cdot 2x = -2 ; end{array}right$

$left{begin{array}{l} y = 2x , 3x - 4x = -2 ; end{array}right$

$left{begin{array}{l} y = 2x , -x = -2 ; end{array}right$

$left{begin{array}{l} y = 2 cdot 2 , x = 2 ; end{array}right$

$left{begin{array}{l} y = 4 , x = 2 ; end{array}right$

Решения удовлетворяют ОДЗ.

О т в е т : $( x ; y ) = ( 2 ; 4 ) .$