Question

Надо решеть систему уравнений
x+y+xy=5
x+y-xy=1

Answer 1

$\tt\displaystyle \left \{ {{x+y+xy=5} \atop {x+y-xy=1|*(-1)}} \right. \Longrightarrow\\\\\\\Longrightarrow +\left \{ {{x+y+xy=5} \atop {-x-y+xy=-1}} \right. \\-----------------\\2xy=4\\xy=2\\\\y=\frac{2}{x}$

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Подставим в 1 уравнение вместо y

$\tt\displaystyle x+\frac{2}{x}+x*\frac{2}{x}=5\\\\\frac{x^2+2}{x}+2=5\\\\\frac{x^2+2}{x}=3\\\\OD3:\ x\neq0\\\\3x=x^2+2\\x^2-3x+2=0\\D=9-4*2*1=9-8=1\\\\x_1=\frac{3-1}{2}=1\\\\\\x_2=\frac{3+1}{2}=2$

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$\tt\displaystyle y=\frac{2}{x}\\\\\\y_1=\frac{2}{1}=2\\\\\\y_2=\frac{2}{2}=1$

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Ответ: (1; 2); (2; 1)