Решить систему уравнений: In x - In y = In3 x-2y=5

[latex] \left \{ {{lnx - lny = ln3} \atop {x - 2y = 5}} \right. \left \{ {{ln \frac{x}{y} = ln3} \atop {x=5 + 2y}} \right. \left \{ {{ \frac{x}{y}=3} \atop {x=5+2y}} \right. [/latex] Заменяем  [latex] \frac{5 +2y}{y} =3 [/latex] [latex] \frac{5+2y}{y} - \frac{3y}{y} = 0[/latex] [latex] \frac{5+2y-3y}{y} = 0[/latex] 5 - y =0 - y = - 5 y = 5 x = 5 + 2y x = 5 + 10 x = 15 Ответ: (15;5)