\(\dfrac{2x}{3}=\dfrac{3y}{4}\)
\(\Leftrightarrow8x=9y\)
\(\Leftrightarrow\dfrac{x}{9}=\dfrac{y}{8}\)
Theo t/c dãy tỉ số bằng nhau ta có :
\(\dfrac{x}{9}=\dfrac{y}{8}=\dfrac{x+y}{9+8}=\dfrac{-17}{17}=-1\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{9}=-1\\\dfrac{y}{8}=-1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=-9\\y=-8\end{matrix}\right.\)
\(\dfrac{2}{3}x=\dfrac{3}{4}y\Leftrightarrow\dfrac{2x}{3}=\dfrac{3y}{4}\)
\(\Leftrightarrow2x.4=3.3y\Leftrightarrow8x=9y\)
\(\Leftrightarrow\dfrac{x}{9}=\dfrac{y}{8}\&x+y=-17\)
Áp dụng tính chất dãy tỉ số bằng nhau:
\(\dfrac{x}{9}=\dfrac{y}{8}=\dfrac{x+y}{9+8}=\dfrac{-17}{17}=-1\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{9}=-1\\\dfrac{y}{8}=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-9\\y=-8\end{matrix}\right.\)
