Từ \(3(x-1)=2(y-2)=3(z-3)\)
\(\Rightarrow\dfrac{x-1}{\dfrac{1}{3}}=\dfrac{y-2}{\dfrac{1}{2}}=\dfrac{z-3}{\dfrac{1}{3}}\)
\(\Rightarrow\dfrac{2x-2}{\dfrac{2}{3}}=\dfrac{4y-8}{2}=\dfrac{z-3}{\dfrac{1}{3}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{2x-2}{\dfrac{2}{3}}=\dfrac{4y-8}{2}=\dfrac{z-3}{\dfrac{1}{3}}=\dfrac{2x-2+4y-8-z+3}{\dfrac{2}{3}+2-\dfrac{1}{3}}\)
\(\dfrac{2x+4y-z-7}{\dfrac{7}{3}}=\dfrac{50-7}{\dfrac{7}{3}}=\dfrac{43}{\dfrac{7}{3}}=\dfrac{129}{7}\)
\(\Rightarrow\left\{{}\begin{matrix}3\left(x-1\right)=\dfrac{129}{7}\\2\left(y-2\right)=\dfrac{129}{7}\\3\left(z-3\right)=\dfrac{129}{7}\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{50}{7}\\y=\dfrac{157}{14}\\z=\dfrac{64}{7}\end{matrix}\right.\)
