Đáp án:
$\left( {x;y;z} \right) = \left( {\dfrac{{5715}}{{53}};\dfrac{{5080}}{{53}};\dfrac{{2667}}{{53}}} \right)$
Giải thích các bước giải:
Ta có:
$\begin{array}{l}
\dfrac{2}{3}x = \dfrac{3}{4}y \Rightarrow \dfrac{2}{9}x = \dfrac{1}{4}y \Rightarrow \dfrac{x}{9} = \dfrac{y}{8} \Rightarrow \dfrac{x}{{45}} = \dfrac{y}{{40}}\\
\dfrac{1}{5}x = \dfrac{3}{7}z \Rightarrow \dfrac{1}{{15}}x = \dfrac{1}{7}z \Rightarrow \dfrac{x}{{15}} = \dfrac{z}{7} \Rightarrow \dfrac{x}{{45}} = \dfrac{z}{{21}}\\
\Rightarrow \dfrac{x}{{45}} = \dfrac{y}{{40}} = \dfrac{z}{{21}}\\
\Rightarrow \dfrac{x}{{45}} = \dfrac{y}{{40}} = \dfrac{z}{{21}} = \dfrac{{3x + 4y - 9z}}{{3.45 + 4.40 - 9.21}} = \dfrac{{254}}{{106}} = \dfrac{{127}}{{53}}\\
\Rightarrow \left\{ \begin{array}{l}
\dfrac{x}{{45}} = \dfrac{{127}}{{53}}\\
\dfrac{y}{{40}} = \dfrac{{127}}{{53}}\\
\dfrac{z}{{21}} = \dfrac{{127}}{{53}}
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = \dfrac{{5715}}{{53}}\\
y = \dfrac{{5080}}{{53}}\\
z = \dfrac{{2667}}{{53}}
\end{array} \right.\\
\Rightarrow \left( {x;y;z} \right) = \left( {\dfrac{{5715}}{{53}};\dfrac{{5080}}{{53}};\dfrac{{2667}}{{53}}} \right)
\end{array}$
Vậy $\left( {x;y;z} \right) = \left( {\dfrac{{5715}}{{53}};\dfrac{{5080}}{{53}};\dfrac{{2667}}{{53}}} \right)$
