\(x+y=\dfrac{x}{y}=5\left(x-y\right)\)
Từ: \(x+y=5\left(x-y\right)=5x-5y\)
\(\Rightarrow5x-5y-x-y=0\)
\(\Rightarrow4x-6y=0\Leftrightarrow2x-3y=0\Leftrightarrow2x=3y\)
\(\Rightarrow\dfrac{x}{y}=\dfrac{3}{2}\)
\(x+y=\dfrac{x}{y}=5\left(x-y\right)\Leftrightarrow x+y=5\left(x-y\right)=\dfrac{3}{2}\)
\(\Rightarrow\left\{{}\begin{matrix}x+y=\dfrac{3}{2}\\x-y=\dfrac{3}{10}\end{matrix}\right.\)
Ok r chứ?
x + y = x : y = 5(x - y)
Từ x + y = 5(x - y)
\(\Leftrightarrow\) x + y = 5x - 5y
\(\Leftrightarrow\) y + 5y = 5x - x
\(\Leftrightarrow\) 6y = 4x
\(\Leftrightarrow\) 3y = 2x
\(\Leftrightarrow\) y = \(\dfrac{2x}{3}\)
\(\Leftrightarrow\) y = \(\dfrac{2}{3}x\)
Mà x + y = x : y (bài cho)
\(\Rightarrow\) x + \(\dfrac{2}{3}x\) = x : \(\dfrac{2}{3}x\)
\(\Leftrightarrow\) \(\dfrac{5}{3}x\) = \(\dfrac{3}{2}\)
\(\Leftrightarrow\) x = \(\dfrac{3}{2}:\dfrac{5}{3}\)
\(\Leftrightarrow\) x = \(\dfrac{9}{10}\)
Mà y = \(\dfrac{2}{3}x\) (chứng minh trên)
\(\Rightarrow\) y = \(\dfrac{2}{3}.\dfrac{9}{10}\)
\(\Leftrightarrow\) y = \(\dfrac{3}{5}\)
Vậy x = \(\dfrac{9}{10}\) ; y = \(\dfrac{3}{5}\)
