Question

\(\left\{{}\begin{matrix}\dfrac{210}{x}-\dfrac{210}{y}=\dfrac{7}{4}\\4x+\dfrac{9}{4}y=210\end{matrix}\right.\)

Answer 1

Đặt: \(\dfrac{1}{x}=a,\dfrac{1}{y}=b\)

ĐKXĐ: \(x,y,a,b\ne0\)

HPT biến đổi thành: \(\left\{{}\begin{matrix}210a-210b=\dfrac{7}{4}\Rightarrow a-b=\dfrac{1}{120}\Rightarrow b=a-\dfrac{1}{120}\\\dfrac{4}{a}+\dfrac{9}{4b}=210\Rightarrow\dfrac{4}{a}+\dfrac{9}{4.\left(a-\dfrac{1}{120}\right)}=210\end{matrix}\right.\)

=> \(a=\dfrac{1}{30},b=\dfrac{1}{40}\)

=> \(\left\{{}\begin{matrix}x=30\\y=40\end{matrix}\right.\)