Đề bài \(\Rightarrow\dfrac{6x}{4}=\dfrac{6y}{9}=\dfrac{6x-6y}{4-9}=\dfrac{6.\left(x-y\right)}{-5}=\dfrac{6.-13}{-5}=\dfrac{78}{5}\Rightarrow\left\{{}\begin{matrix}x=\dfrac{52}{5}\\y=\dfrac{117}{5}\end{matrix}\right.\)
Có :`(3x)/2=(2y)/3` `(1)`
`x-y=-13`
`->x=y-13`
Thay `x=y-13` vào `(1)` , ta có :
`(3(y-13))/2=(2y)/3`
`->9(y-13)=4y`
`->9y-117=4y`
`->5y=117`
`->y=117/5`
`->x=117/5 - 13=52/5`
Ta có: \(\dfrac{3x}{2}=\dfrac{2y}{3}\)
nên \(x\cdot\dfrac{3}{2}=y\cdot\dfrac{2}{3}\)
\(\Leftrightarrow\dfrac{x}{\dfrac{2}{3}}=\dfrac{y}{\dfrac{3}{2}}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{x}{\dfrac{2}{3}}=\dfrac{y}{\dfrac{3}{2}}=\dfrac{x-y}{\dfrac{2}{3}-\dfrac{3}{2}}=\dfrac{-13}{\dfrac{-5}{6}}=\dfrac{78}{5}\)
Do đó:
\(\left\{{}\begin{matrix}x=\dfrac{78}{5}\cdot\dfrac{2}{3}=\dfrac{52}{5}\\y=\dfrac{78}{5}\cdot\dfrac{3}{2}=\dfrac{117}{5}\end{matrix}\right.\)
