Question

Tìm x,y biết:

\(\frac{2}{x-1}=\frac{3}{y-2}=\frac{4}{z.3}\)và 2x +3y-z=95

Answer 1

\(\frac{2}{x-1}=\frac{3}{y-2}=\frac{4}{z.3}\)

=> \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{3.z}{4}\)

=> \(\frac{2\left(x-1\right)}{2.2}=\frac{3\left(y-2\right)}{3.3}=\frac{3z:3}{4:3}\)

=> \(\frac{2x-2}{4}=\frac{3y-6}{9}=\frac{z}{\frac{4}{3}}=\frac{2x-2+3y-6-z}{4+9-\frac{4}{3}}=\frac{\left(2x+3y-z\right)-8}{\frac{35}{3}}=\frac{95-8}{\frac{35}{3}}=\frac{261}{35}\)

=> \(\hept{\begin{cases}\frac{2x-2}{4}=\frac{261}{35}\\\frac{3y-6}{9}=\frac{261}{35}\\\frac{z}{\frac{4}{3}}=\frac{261}{35}\end{cases}\Leftrightarrow\hept{\begin{cases}x=\frac{557}{35}\\y=\frac{853}{35}\\z=\frac{348}{35}\end{cases}}}\)