\(If $a,b,c$ are positive integers less than $13$ such that \begin{align*} 2ab+bc+ca&\equiv 0\pmod{13}\\ ab+2bc+ca&\equiv 6abc\pmod{13}\\ ab+bc+2ca&\equiv 8abc\pmod {13} \end{align*}then determine the remainder when $a+b+c$ is divided by $13$.\)

Please help I really am bad at these sorts of things.

Thanks!

Guest Jan 5, 2019