Question

\(\dfrac{x+5}{2}=\dfrac{y-2}{3},x-y=-10\)

Answer 1

Vì \(\dfrac{x+5}{2}=\dfrac{y-2}{3}\)

Mà \(x-y=-10\)

Áp dụng tính chất của dãy tỉ số bằng nhau

\(\Rightarrow\dfrac{x+5}{2}=\dfrac{y-2}{3}=\dfrac{\left(x+5\right)-\left(y-2\right)}{2-3}=\dfrac{x+5-y+2}{-1}=\dfrac{\left(x-y\right)+\left(5+2\right)}{-1}=\dfrac{\left(-10\right)+7}{-1}=\dfrac{-3}{-1}=3\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x+5}{2}=3\\\dfrac{y-2}{3}=3\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x+5=6\\y-2=9\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=1\\y=11\end{matrix}\right.\)

Vậy \(\left\{{}\begin{matrix}x=1\\y=11\end{matrix}\right.\).