Question

Giải HPT sau bằng Pp đặt ẩn phụ :

\(\left\{{}\begin{matrix}\frac{3}{5x}+\frac{1}{y}=10\\\frac{3}{4x}+\frac{3}{4y}=\frac{1}{12}\end{matrix}\right.\)

Answer 1

ĐKXĐ: ...

Đặt \(\left\{{}\begin{matrix}\frac{1}{x}=u\\\frac{1}{y}=v\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\frac{3}{5}u+v=10\\\frac{3}{4}u+\frac{3}{4}v=12\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}3u+5v=50\\3u+3v=48\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}v=1\\u=15\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\frac{1}{x}=15\\\frac{1}{y}=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=\frac{1}{15}\\y=1\end{matrix}\right.\)