Question

Tìm x,y biết

\(\dfrac{3x+2}{4}=\dfrac{2y+2}{5}=\dfrac{3x+2y+4}{4,5x}\left(x\ne0\right)\)

Gấp gấp bài này có 2 trường hợp nhá!!

Answer 1

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{3x+2}{4}=\dfrac{2y+2}{5}=\dfrac{3x+2y+4}{4,5x}=\dfrac{3x+2+2y+2-3x-2y-4}{4+5-4,5x}=\dfrac{0}{9-4,5x}=0\)

\(\Rightarrow\left\{{}\begin{matrix}3x+2=0\\2y+2=0\\3x+2y+4=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x=-2\\2y=-2\\3x+2y=-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{2}{3}\\y=-1\end{matrix}\right.\)

Answer 2

Áp dụng t/c dãy tỉ số bằng nhau :

\(\dfrac{3x+2}{4}=\dfrac{2y+2}{5}=\dfrac{3x+2+2y+2}{4+5}=\dfrac{3x+2y+4}{9}\)

Mà \(\dfrac{3x+2}{4}=\dfrac{2y+2}{5}=\dfrac{3x+2y+4}{4,5x}\)

=> \(\dfrac{3x+2y+4}{9}=\dfrac{3x+2y+4}{4,5x}\)

=> 9 = 4,5x

=> x = 9 : 4,5 = 2

Ta có : \(\dfrac{3x+2}{4}=\dfrac{2y+2}{5}\)

\(\dfrac{3.2+2}{4}=\dfrac{2y+2}{5}\) ( Thay x = 2)

\(2=\dfrac{2y+2}{5}\)

=> 2y = 2.5 - 2 = 8

=> y = 8 : 2 = 4

Vậy x = 2, y = 4