Determine \(3x_{4}+2x_{5}\), if \(x_{1},x_{2},x_{3},x_{4},x_{5}\) satisfy the system of equations:

\(\left\{\begin{matrix}2x_{1}+x_{2}+x_{3}+x_{4}+x_{5}=6,\\ x_{1}+2x_{2}+x_{3}+x_{4}+x_{5}=12,\\ x_{1}+x_{2}+2x_{3}+x_{4}+x_{5}=24,\\ x_{1}+x_{2}+x_{3}+2x_{4}+x_{5}=48,\\ x_{1}+x_{2}+x_{3}+x_{4}+2x_{5}=96,\end{matrix}\right.\)

(第四届AIME1986 第4题)