Question

`x/4 - y/3 ; y/5 = z/3 ` và` x+y-z=-100`

Answer 1

\(\dfrac{x}{4}-\dfrac{y}{3};\dfrac{y}{5}=\dfrac{z}{3},x+y-z=-100\)

\(\Rightarrow\dfrac{x}{20}=\dfrac{y}{15};\dfrac{y}{15}=\dfrac{z}{9},x+y-z=-100\)

\(\Leftrightarrow\dfrac{x}{20}=\dfrac{y}{15}=\dfrac{z}{9},x+y-z=-100\)

Áp dụng tính chất dãy tỉ số bằng nhau:

\(\dfrac{x}{20}=\dfrac{y}{15}=\dfrac{z}{9}=\dfrac{x+y-z}{20+15-9}=\dfrac{-100}{26}=-\dfrac{50}{13}\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{20}=-\dfrac{50}{13}\Leftrightarrow x=-\dfrac{1000}{13}\\\dfrac{y}{15}=-\dfrac{50}{13}\Leftrightarrow y=-\dfrac{750}{13}\\\dfrac{z}{9}=-\dfrac{50}{13}\Leftrightarrow z=-\dfrac{450}{13}\end{matrix}\right.\)