Question

Giải hpt bằng pp đặt ẩn phụ

x/(x-3) + 3y/(y-1) = 5

4x/(x-3) - y/(y-1) = 7

Answer 1

ĐKXĐ:\(\left\{{}\begin{matrix}x\ne3\\y\ne1\end{matrix}\right.\)

Đặt `(x)/(x-3)` = a, `(y)/(y-1)` = b

  \(\text{Hệ}\Leftrightarrow\left\{{}\begin{matrix}a+3b=5\\4a-b=7\end{matrix}\right.\\ \Leftrightarrow...\\ \Leftrightarrow\left\{{}\begin{matrix}a=2\\b=1\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{x-3}=2\\\dfrac{y}{y-1}=1\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=2x-6\\y=y-1\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=6\\-1=0\left(vô.lí\right)\end{matrix}\right.\)

Vậy hpt vô nghiệm