Question

giải hệ phương trình

\(\left\{{}\begin{matrix}\dfrac{2x-3}{x-2}+\dfrac{y+7}{y+3}=5\\\dfrac{x+1}{x-2}+\dfrac{3y+1}{y+3}=5\end{matrix}\right.\)

Answer 1

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2x-4+1}{x-2}+\dfrac{y+3+4}{y+3}=5\\\dfrac{x-2+3}{x-2}+\dfrac{3y+9-8}{y+3}=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x-2}+\dfrac{4}{y+3}=5-1-2=2\\\dfrac{3}{x-2}+\dfrac{-8}{y+3}=5-1-3=1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-2=1\\y+3=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)