\(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}\Rightarrow\dfrac{5\left(z-5\right)}{30}=\dfrac{3\left(x-1\right)}{6}=\dfrac{4\left(y+3\right)}{16}=\dfrac{5\left(z-5\right)-3\left(x-1\right)-4\left(y+3\right)}{30-6-16}=\dfrac{5z-25-3x+3-4y-12}{8}=\dfrac{\left(5z-3x-4y\right)+\left(-25+3-12\right)}{8}=\dfrac{50+\left(-34\right)}{8}=\dfrac{16}{8}=2\)\(\Rightarrow\dfrac{x-1}{2}=2\Rightarrow x=5\\ \dfrac{y+3}{4}=4\Rightarrow y=13\\ \dfrac{z-5}{6}=2\Rightarrow z=17\)
Theo bài ra ta có :
\(\dfrac{x-1}{2}=\dfrac{y+3}{4}=\dfrac{z-5}{6}\\ \Rightarrow\dfrac{3\left(x-1\right)}{6}=\dfrac{4\left(y+3\right)}{16}=\dfrac{5\left(z-5\right)}{30}\\ \Rightarrow\dfrac{3x-3}{6}=\dfrac{4y+12}{16}=\dfrac{5z-25}{30}\\ \Rightarrow\dfrac{5z-25}{30}=\dfrac{3x-3}{6}=\dfrac{4y+12}{16}\)
\(5z-3x-4y=50\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được :
\(\dfrac{5z-25}{30}=\dfrac{3x-3}{6}=\dfrac{4y+12}{16}\\ =\dfrac{\left(5z-25\right)-\left(3x-3\right)-\left(4y+12\right)}{30-6-16}\\ =\dfrac{5z-25-3x+3-4y-12}{8}\\ =\dfrac{\left(5z-3x-4y\right)-\left(25-3+12\right)}{8}\\ =\dfrac{50-34}{8}\\ =\dfrac{16}{8}\\ =2\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{3x-3}{6}=2\Rightarrow3x-3=12\Rightarrow3x=15\Rightarrow x=5\\\dfrac{4y+12}{16}=2\Rightarrow4y+12=32\Rightarrow4y=20\Rightarrow y=5\\\dfrac{5z-25}{30}=2\Rightarrow5z-25=60\Rightarrow5z=85\Rightarrow z=17\end{matrix}\right.\)
\(\text{Vậy }x=5\\ y=5\\ z=17\)
