Question

розв'яжіть систему рівнянь​

Answer 1

$\left \{ {{xy-\frac{y}{x} =6} \atop {3xy+\frac{2y}{x} =28}} \right.$

Сделаем замену :

$xy=a\\\\\frac{y}{x}=b\\\\\left \{ {{a-b=6}|*2 \atop {3a+2b=28}} \right.\\\\+\left \{ {{2a-2b=12} \atop {3a+2b=28}} \right.\\ -------\\5a=40\\\\a=8\\\\b=a-6=8-6=2\\\\\left \{ {{xy=8} \atop {\frac{y}{x} }=2} \right\\\\\left \{ {{y=2x} \atop {x*2x=8}} \right.\\\\\left \{ {{y=2x} \atop {2x^{2}=8 }} \right.$

$\left \{ {{y=2x} \atop {x^{2} =4}} \right.\\\\\left \{ {{x_{1}=-2 } \atop {y_{1} =-4}} \right.\\\\\left \{ {{x_{2} =2} \atop {y_{2}=4 }} \right.$

Ответ : (- 2 ; - 4) , (2 ; 4)