Question

Giair hệ phương trình sau:

\(\hept{\begin{cases}\frac{4}{y-3}+\frac{3}{x+4}=9\\\frac{3}{y-3}-\frac{5}{x+4}=14\end{cases}}\)

Answer 1

Hệ     ĐK \(y\ne3;x\ne-4\)

\(\Leftrightarrow\hept{\begin{cases}\frac{12}{y-3}+\frac{9}{x+4}=27\\\frac{12}{y-3}-\frac{20}{x+4}=56\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}\frac{29}{x+4}=-29\\\frac{4}{y-3}+\frac{3}{x+4}=9\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}\frac{1}{x+4}=-1\\\frac{1}{y-3}=3\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x+4=-1\\y-3=\frac{1}{3}\end{cases}\Leftrightarrow\hept{\begin{cases}x=-5\\y=\frac{10}{3}\end{cases}\left(tm\right)}}\)

Vậy HPT có nghiệm ( -5; 10/3)