Question

Решите систему уравнений​

Answer 1

Ответ:

$\bigg (\dfrac{1}{4}; \dfrac{1}{3} \bigg ) \quad ; \quad \bigg (\dfrac{1}{3}; \dfrac{1}{4} \bigg ) \quad ;$

Объяснение:

ОДЗ:

$x \neq 0, \quad y \neq 0;$

Решение:

$\displaystyle \left \{ {{\dfrac{1}{x}+\dfrac{1}{y}=7} \atop {x+5xy+y=1}} \right. \Leftrightarrow \left \{ {{\dfrac{y+x}{xy}=7} \atop {x+5xy+y=1}} \right. \Leftrightarrow \left \{ {{x+y=7xy} \atop {x+y=1-5xy}} \right. \Leftrightarrow$

$\displaystyle \Leftrightarrow \left \{ {{1-5xy=7xy} \atop {x+y=1-5xy}} \right. \Leftrightarrow \left \{ {{12xy=1} \atop {x+y=1-5xy}} \right. \Leftrightarrow \left \{ {{xy=\dfrac{1}{12}} \atop {x+y=1-\dfrac{5}{12}}} \right. \Leftrightarrow$

$\displaystyle \Leftrightarrow \left \{ {{xy=\dfrac{1}{12}} \atop {x+y=\dfrac{7}{12}}} \right. \Leftrightarrow \left \{ {{x=\dfrac{1}{4}} \atop {y=\dfrac{1}{3}}} \right. \quad \vee \quad \left \{ {{x=\dfrac{1}{3}} \atop {y=\dfrac{1}{4}}} \right. ;$

$\bigg (\dfrac{1}{4}; \dfrac{1}{3} \bigg ); \bigg (\dfrac{1}{3}; \dfrac{1}{4} \bigg );$