Bài 1 a) \(\dfrac{x}{2}=\dfrac{y}{5}\) \(\text{Mà }x+y=-14\) Áp dụng t/c dãy tỉ số bằng nhau ta có: \(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{x+y}{2+5}=\dfrac{-14}{7}=-2\) \(\Rightarrow\dfrac{x}{2}=-2\Rightarrow x=2.\left(-2\right)=-4\) \(\Rightarrow\dfrac{y}{5}=-2\Rightarrow y=5.\left(-2\right)=-10\) \(\text{Vậy }\left\{{}\begin{matrix}x=-4\\y=-10\end{matrix}\right.\) b) \(\dfrac{x}{7}=\dfrac{y}{5}\) \(\text{Mà }x-y=8\) Áp dụng t/c dãy tỉ số bằng nhau ta có: \(\dfrac{x}{7}=\dfrac{y}{5}=\dfrac{x-y}{7-5}=\dfrac{8}{2}=4\) \(\Rightarrow\dfrac{x}{7}=4\Rightarrow x=4.7=28\) \(\Rightarrow\dfrac{y}{5}=4\Rightarrow y=4.5=20\) \(\text{Vậy }\left\{{}\begin{matrix}x=28\\y=20\end{matrix}\right.\) Bài 2: a) \(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7}\) \(\text{Mà }x+y+z=56\) Áp dụng t/c dãy tỉ số bằng nhau ta có: \(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{z}{7}=\dfrac{x+y+z}{2+5+7}=\dfrac{56}{14}=4\) \(\Rightarrow\dfrac{x}{2}=4\Rightarrow x=4.2=8\) \(\Rightarrow\dfrac{y}{5}=4\Rightarrow y=4.5=20\) \(\Rightarrow\dfrac{z}{7}=4\Rightarrow z=4.7=28\) \(\text{Vậy }\left\{{}\begin{matrix}x=8\\y=20\\z=28\end{matrix}\right.\) b) \(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{8}\) \(\Rightarrow\dfrac{2x}{6}=\dfrac{y}{5}=\dfrac{z}{8}\) \(\text{Mà }2x+y-z=12\) Áp dụng t/c dãy tỉ số bằng nhau ta có: \(\dfrac{2x}{6}=\dfrac{y}{5}=\dfrac{z}{8}=\dfrac{2x+y-z}{6+5-8}=\dfrac{12}{3}=4\) \(\Rightarrow\dfrac{2x}{6}=4\Rightarrow2x=4.6=24\Rightarrow x=24:2=12\) \(\Rightarrow\dfrac{y}{5}=4\Rightarrow y=4.5=20\) \(\Rightarrow\dfrac{z}{8}=4\Rightarrow z=4.8=32\) \(\text{Vậy }\left\{{}\begin{matrix}x=12\\y=20\\z=32\end{matrix}\right.\)