Question

giúp ạ!

Answer 1

\(y-x=4< =>y=4+x\)

Thay y=4+x vào biểu thức ta được:

\(\frac{x-5}{y-7}=\frac{5}{7}\\ < =>\frac{x-5}{x+4-7}=\frac{5}{7}\\ < =>\frac{x-5}{x-3}=\frac{5}{7}\\ =>7\left(x-5\right)=5\left(x-3\right)\\ < =>7x-35=5x-15\\ < =>2x=20\\ =>x=10\\ =>y=x+4=10+4=14\\ Vậy:x+y=10+14=24\)

Answer 2

\(\dfrac{x-5}{y-7}=\dfrac{5}{7}\\ \Rightarrow\dfrac{x-5}{5}=\dfrac{y-7}{7}\)

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

\(\dfrac{x-5}{5}=\dfrac{y-7}{7}=\dfrac{y-7-x+5}{7-5}=\dfrac{4-7+5}{2}=\dfrac{2}{2}=1\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x+5}{5}=1\\\dfrac{y-7}{7}=1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x+5=1\cdot5=5\\y-7=1\cdot7=7\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=5-5=0\\y=7+7=14\end{matrix}\right.\)\(\Rightarrow x+y=0+14=14\)