Surprisingly Sufficient Information

Algebra Level 2

\[\large{ \begin{cases} 5a+3b+c=17 \\ 1a + 4b+7c=21 \end{cases}} \]

Given that \(a,b\) and \(c\) satisfy the system of equations above, and \(a+b+c\) is equal to \( \dfrac xy \), where \(x\) and \(y\) are coprime positive integers, find \(x+y\).

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