6/11x=9/2y=18/5z và -x+y+z=-120

Đáp án:

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

$\begin{array}{l}
\dfrac{6}{{11x}} = \dfrac{9}{{2y}} = \dfrac{{18}}{{5z}}\\
 \Rightarrow \dfrac{{11x}}{6} = \dfrac{{2y}}{9} = \dfrac{{5z}}{{18}}\\
 \Rightarrow \dfrac{x}{{\dfrac{6}{{11}}}} = \dfrac{y}{{\dfrac{9}{2}}} = \dfrac{z}{{\dfrac{{18}}{5}}} = \dfrac{{ - x + y + z}}{{\dfrac{{ - 6}}{{11}} + \dfrac{9}{2} + \dfrac{{18}}{5}}}\\
 = \dfrac{{ - 120}}{{\dfrac{{831}}{{110}}}} = \dfrac{{ - 4400}}{{277}}\\
 \Rightarrow \left\{ \begin{array}{l}
x = \dfrac{{ - 4400}}{{277}}.\dfrac{6}{{11}} = \dfrac{{ - 2400}}{{277}}\\
y = \dfrac{{ - 4400}}{{277}}.\dfrac{9}{2} =  - \dfrac{{19800}}{{277}}\\
z = \dfrac{{ - 4400}}{{277}}.\dfrac{{18}}{5} =  - \dfrac{{15840}}{{277}}
\end{array} \right.
\end{array}$