\(\left\{{}\begin{matrix}\dfrac{x}{y}=2\\x=3z\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2y\\x=3z\end{matrix}\right.\Leftrightarrow x=2y=3z\)

\(\Rightarrow4x=8y=12z=10\)

\(\Rightarrow x+y+z=\dfrac{10}{4}+\dfrac{10}{8}+\dfrac{10}{12}=\dfrac{55}{12}\)