Determine 3 x_{4}+2 x_{5} if x_{1}, x_{2}, x_{3}, x_{4} and x_{5} satisfy the system of equations given below:
\begin{aligned}
2 x_{1}+x_{2}+x_{3}+x_{4}+x_{5}= & 6 \\
x_{1}+2 x_{2}+x_{3}+x_{4}+x_{5}= & 12 \\
x_{1}+x_{2}+2 x_{3}+x_{4}+x_{5}= & 24 \\
x_{1}+x_{2}+x_{3}+2 x_{4}+x_{5}= & 48 \\
x_{1}+x_{2}+x_{3}+x_{4}+2 x_{5}= & 96
\end{aligned}