Question

Giải hệ phương trình

\(\left\{{}\begin{matrix}12x+12y=1\\4x+14y=1\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}12x+12y=1\\4x+14y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+y=\dfrac{1}{12}\\x+\dfrac{7}{2}y=\dfrac{1}{4}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{5}{2}y=\dfrac{1}{6}\\x+y=\dfrac{1}{12}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{1}{15}\\x+y=\dfrac{1}{12}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{60}\\y=\dfrac{1}{15}\end{matrix}\right.\)

Vậy hệ phương trình có nghiệm \(x=\dfrac{1}{60},y=\dfrac{1}{15}\)