Question

Помогите срочно!!
Розв'яжіть систему рівнянь:

Answer 1

Сделаем замену :

$\frac{x}{y} =m\Rightarrow \frac{y}{x}=\frac{1}{m}\\\\\frac{x}{y}+\frac{y}{x}=2\frac{1}{2}\\\\m+\frac{1}{m}-\frac{5}{2}=0,m\neq0 \\\\2m^{2}-5m+2=0\\\\D=(-5)^{2}-4*2*2=25-16=9=3^{2}\\\\m_{1}=\frac{5-3}{4}=\frac{1}{2}\\\\m_{2}=\frac{5+3}{4}=2$

$1)\left \{ {{\frac{x}{y}=\frac{1}{2}} \atop {2x-3y=3}} \right.\\\\\left \{ {{y=2x} \atop {2x-3*2x=3}} \right.\\\\\left \{ {{y=2x} \atop {-4x=3}} \right. \\\\\left \{ {{x=-0,75} \atop {y=-1,5}} \right.$

$2)\left \{ {{\frac{x}{y}=2} \atop {2x-3y=3}} \right.\\\\\left \{ {{x=2y} \atop {2*2y-3y=3}} \right.\\\\\left \{ {{x=2y} \atop {y=3}} \right. \\\\\left \{ {{x=6} \atop {y=3}} \right.\\\\Otvet:\boxed{(-0,75;-1,5),(6;3)}$