Question

Решите систему уравнений сетодом замены переменной {(1/x+3y)+y=5 {y/(x+3y)=6

Answer 1

$\left \{ {{\frac{1}{x} + y = 5} \atop {\frac{y}{x + 3y} = 6}} \right. \:\:=\ \textgreater \ \:\: \left \{ {{y = 5 - \frac{1}{x}} \atop {\frac{y}{x + 3y} = 6}} \right. \:\:=\ \textgreater \ \:\: \left \{ {{y = 5 - \frac{1}{x}} \atop {\frac{5 - \frac{1}{x}}{x + 3(5 - \frac{1}{x})} = 6}} \right. \:\:=\ \textgreater \ \:\:$
$\left \{ {{y = 5 - \frac{1}{x}} \atop {5 - \frac{1}{x} = 6x + 18(5 - \frac{1}{x})}} \right. \:\:=\ \textgreater \ \:\: \left \{ {{y = 5 - \frac{1}{x}} \atop {5 - \frac{1}{x} = 6x + 90 - \frac{18}{x}}} \right. \:\:=\ \textgreater \ \:\: \left \{ {{y = 5 - \frac{1}{x}} \atop {6x + 85 - \frac{17}{x}} = 0} \right.\\ 6x^2 + 85*x - 17 = 0\\$
$6x^2 + 85x - 17 = 0\\ x_1 = \frac{-85+\sqrt{7633}}{12} \: y_1=\\ x_2 = \frac{-85-\sqrt{7633}}{12} \: y_2=\\$