Question

giải hệ phương trình \(\left\{{}\begin{matrix}\frac{5}{x-2}-\frac{2y-4}{y-3}=2\\\frac{x+2}{x-2}-\frac{2}{y-3}=4\end{matrix}\right.\)

Answer 1

ĐKXĐ: ....

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

\(\Rightarrow\frac{1}{x-2}=1\Rightarrow x-2=1\Rightarrow x=3\)

\(\Rightarrow\frac{2}{y-3}=\frac{5}{x-2}-4=1\Rightarrow y-3=2\Rightarrow y=5\)

Nghiệm của hệ \(\left(x;y\right)=\left(3;5\right)\)