\(Given that \begin{align*} 5a - 7b + 3c &= 19, \\ 2a - 4b + c &= 77,\end{align*} determine the value of $a+b+c$.\)
5a - 7b + 3c = 19 ---> 5a - 7b + 3c = 19
2a - 4b + c = 77 ---> multiply by -2 ---> -4a + 8b - 2c = -154
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Add down the columns: a + b + c = -135
+1836 
