Đáp án:
\(\left\{ \begin{array}{l}
x = \frac{{18}}{{11}}.10 = \frac{{180}}{{11}}\\
y = \frac{{18}}{{11}}.6 = \frac{{108}}{{11}}\\
z = \frac{{18}}{{11}}.5 = \frac{{90}}{{11}}
\end{array} \right.\)
Giải thích các bước giải:
\[\begin{array}{l}
3x = 5y;\,\,\,5y = 6z;\,\,\,x + y - z = 18\\
Ta\,\,co:\\
3x = 5y;\,\,\,5y = 6z\\
\Rightarrow 3x = 5y = 6z\\
\Rightarrow \frac{x}{{10}} = \frac{y}{6} = \frac{z}{5}\\
Ap\,\,dung\,\,tinh\,\,chat\,\,\,cua\,\,\,day\,\,\,ti\,\,\,so\,\,bang\,\,nhau\,\,ta\,\,co:\\
\frac{x}{{10}} = \frac{y}{6} = \frac{z}{5} = \frac{{x + y - z}}{{10 + 6 - 5}} = \frac{{18}}{{11}}\\
\Rightarrow \left\{ \begin{array}{l}
x = \frac{{18}}{{11}}.10 = \frac{{180}}{{11}}\\
y = \frac{{18}}{{11}}.6 = \frac{{108}}{{11}}\\
z = \frac{{18}}{{11}}.5 = \frac{{90}}{{11}}
\end{array} \right..
\end{array}\]
