Question

\(\left\{{}\begin{matrix}3x^2-8xy+5y^2=0\\2x+7y=5\end{matrix}\right.\)

Answer 1

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-y\right)\left(3x-5y\right)=0\\2x+7y=5\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-y=0\\2x+7y=5\end{matrix}\right.\\\left\{{}\begin{matrix}3x-5y=0\\2x+7y=5\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=\frac{5}{9}\\y=\frac{5}{9}\end{matrix}\right.\\\left\{{}\begin{matrix}x=\frac{25}{31}\\x=\frac{15}{31}\end{matrix}\right.\end{matrix}\right.\)