TIMO - 2020 - Grade 9 - Heat Round - Paper 2 Question 9

Find $c$ in $\begin{cases}6a+b+c+d+e=16\\a+6b+c+d+e=18\\a+b+6c+d+e=20\\a+b+c+6d+e=22\\a+b+c+d+6e=24\end{cases}$.