\(\left\{{}\begin{matrix}x=\dfrac{5}{9}y\\x=\dfrac{10}{21}z\\2x=3y+z=50\end{matrix}\right.\)\(\Rightarrow2x-\dfrac{27}{5}+\dfrac{21}{10}x=50\)
\(\left\{{}\begin{matrix}x=\dfrac{500}{15}\\y=-\dfrac{900}{13}\\-\dfrac{1050}{13}\end{matrix}\right.\)
b: Ta có: \(\dfrac{x}{-3}=\dfrac{y}{7}\)
nên \(\dfrac{x}{6}=\dfrac{y}{-14}\left(1\right)\)
Ta có: \(\dfrac{y}{-2}=\dfrac{z}{5}\)
nên \(\dfrac{y}{-14}=\dfrac{z}{35}\left(2\right)\)
Từ \(\left(1\right),\left(2\right)\) suy ra \(\dfrac{x}{6}=\dfrac{y}{-14}=\dfrac{z}{35}\)
hay \(\dfrac{-2x}{12}=\dfrac{4y}{-56}=\dfrac{5z}{175}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{-2x}{12}=\dfrac{4y}{-56}=\dfrac{5z}{175}=\dfrac{-2x-4y+5z}{12+56+175}=\dfrac{146}{243}\)
Do đó: \(\left\{{}\begin{matrix}x=\dfrac{292}{81}\\y=-\dfrac{2044}{243}\\z=\dfrac{5110}{243}\end{matrix}\right.\)
