Ta có:
\(\left\{{}\begin{matrix}x.\left(x-y\right)=\frac{3}{10}\left(1\right)\\y.\left(x-y\right)=-\frac{3}{50}\left(2\right)\end{matrix}\right.\)
Lấy vế \(\left(1\right)\) chia theo vế cho \(\left(2\right)\) ta được:
\(\frac{x.\left(x-y\right)}{y.\left(x-y\right)}=\frac{x}{y}=\frac{3}{10}:\left(-\frac{3}{50}\right)=-5.\)
\(\frac{x}{y}=-5\Rightarrow x=-5y\left(3\right)\)
Thay \(\left(3\right)\) vào \(\left(2\right)\) ta được:
\(y.\left(-5y-y\right)=-\frac{3}{50}\)
\(\Rightarrow-6y^2=-\frac{3}{50}.\)
\(\Rightarrow y^2=\left(-\frac{3}{50}\right):\left(-6\right)\)
\(\Rightarrow y^2=\frac{1}{100}\)
\(\Rightarrow\left[{}\begin{matrix}y=\frac{1}{10}\Rightarrow x=\frac{1}{2}\\y=-\frac{1}{10}\Rightarrow x=-\frac{1}{2}\end{matrix}\right.\)
Vậy \(\left(x;y\right)=\left(\frac{1}{10};\frac{1}{2}\right),\left(-\frac{1}{10};-\frac{1}{2}\right).\)
Chúc bạn học tốt!
