Question

giải hệ pt 

x+y/2 =x-y/4

x/3=y/5+1

Answer 1

\(\left\{{}\begin{matrix}\dfrac{x+y}{2}=\dfrac{x-y}{4}\\\dfrac{x}{3}=\dfrac{y}{5}+1\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}2\left(x+y\right)=x-y\\5x=3y+15\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}2x+2y-x+y=0\\5x-3y=15\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x+3y=0\\5x-3y=15\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+3y+5x-3y=15\\x+3y=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}6x=15\\x+3y=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=2,5\\3y=-x=-2,5\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=2,5\\y=-\dfrac{2.5}{3}=-\dfrac{5}{6}\end{matrix}\right.\)