Question

система lgx+lg2=lgy 3х-2у=-2

Answer 1

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 :    $( x ; y ) = ( 2 ; 4 ) \ .$