Problem: Determine $3 x_4+2 x_5$ if $x_1, x_2, x_3, x_4$, and $x_5$ satisfy the system of equations below. $ \begin{gathered} 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{gathered} $ Solution: Add all the equations and divide by $6$ on both sides to get that $\sum x_i = 31$. Then, subtract this sum from the fifth equation to get $x_2 = 65$ meaning $2x_2 = 130$. Do the same for the fourth equation to get $x_4 = 17$ meaning $3x_4 = 51$. Our final answer is thus $181$.