Question

[nguyễn ngọc bảo hân]

giup mik voi

Tìm m,n để hệ PT {2(m+1)x-7(n-2)y=6

                             (m+1)x+(n-2)y=12

Answer 1

[HT.Phong (9A5)]

\(\left\{{}\begin{matrix}2\left(m+1\right)x-7\left(n-2\right)y=6\\\left(m+1\right)x+\left(n-2\right)y=12\end{matrix}\right.\left(m\ne-1;n\ne2\right)\)

\(\Leftrightarrow\left\{{}\begin{matrix}2\left(m+1\right)x-7\left(n-2\right)y=6\\2\left(m+1\right)x+2\left(n-2\right)y=24\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}9\left(n-2\right)y=-18\\\left(m+1\right)x+\left(n-2\right)y=12\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{-18}{9\left(n-2\right)}=\dfrac{-2}{n-2}\\\left(m+1\right)x+\left(n-2\right)\cdot\dfrac{-2}{n-2}=24\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{2}{n-2}\\\left(m+1\right)x-2=24\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{-2}{n-2}\\\left(m+1\right)x=26\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{-2}{n-2}\\x=\dfrac{26}{m+1}\end{matrix}\right.\)