a) \(\dfrac{7}{x}=\dfrac{5}{y}\Rightarrow\dfrac{x}{7}=\dfrac{y}{5}=\dfrac{y-x}{5-7}=\dfrac{10}{-2}=-5\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{7}=-5\\\dfrac{y}{5}=-5\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-35\\y=-25\end{matrix}\right.\)
b) \(\dfrac{x}{3}=\dfrac{y}{5}=k\Rightarrow\dfrac{x}{3}.\dfrac{y}{5}=k^2\Rightarrow k^2=\dfrac{xy}{15}=\dfrac{60}{15}=4\Rightarrow k=\pm2\)
Với \(k=2\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{3}=2\\\dfrac{y}{5}=2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=6\\y=10\end{matrix}\right.\)
Với \(k=-2\Rightarrow\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{3}=-2\\\dfrac{y}{5}=-2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-6\\x=-10\end{matrix}\right.\)
c) \(\dfrac{x-3}{2}=\dfrac{4+x}{3}\Rightarrow3\left(x-3\right)=2\left(4+x\right)\Rightarrow3x-9=6+2x\Rightarrow x=15\)
d) \(\dfrac{x-2}{4}=\dfrac{-9}{2-x}\Rightarrow\dfrac{x-2}{4}=\dfrac{9}{x-2}\Rightarrow\left(x-2\right)^2=36\Rightarrow\left[{}\begin{matrix}x-2=6\\x-2=-6\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=8\\x=-4\end{matrix}\right.\)
e) \(5x=3y=6z\Rightarrow\dfrac{5x}{5.3.6}=\dfrac{3y}{5.3.6}=\dfrac{6z}{5.3.6}\)
\(\Rightarrow\dfrac{x}{18}=\dfrac{y}{30}=\dfrac{z}{15}=\dfrac{2x-y+z}{2.18-30+15}=\dfrac{-14}{21}=-\dfrac{2}{3}\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{18}=-\dfrac{2}{3}\\\dfrac{y}{30}=-\dfrac{2}{3}\\\dfrac{z}{15}=-\dfrac{2}{3}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-12\\y=-20\\z=-10\end{matrix}\right.\)
Câu f tương tự câu e bạn tự làm nhé!