Vì \(\dfrac{x+2y}{4x-3y}=-2\) nên:
\(x+2y=-2\left(4x-3y\right)\\ \Rightarrow x+2y=-8x-\left(-6y\right)\\ \Rightarrow x+2y=-8x+6y\\ \Rightarrow x+8x=6y-2y\\ \Rightarrow9x=4y\)
\(\Rightarrow\dfrac{x}{4}=\dfrac{y}{9}\\ \Rightarrow\dfrac{x}{y}=\dfrac{4}{9}\)
Vậy: \(\dfrac{x}{y}=\dfrac{4}{9}\)
Ta có: \(\dfrac{x+2y}{4x-3y}=-2\)
\(\Rightarrow x+2y=\left(4x-3y\right)\left(-2\right)\)
\(\Rightarrow x+2y=-8x+6y\)
\(\Rightarrow x+8x=-2y+6y\)
\(\Rightarrow9x=4y\)
\(\Rightarrow\dfrac{x}{y}=\dfrac{4}{9}\)
Vậy \(\dfrac{x}{y}=\dfrac{4}{9}\) khi \(y\ne0.\)