Surprisingly Sufficient Information

Algebra Level 2

{5a+3b+c=171a+4b+7c=21\large{ \begin{cases} 5a+3b+c=17 \\ 1a + 4b+7c=21 \end{cases}}

Given that a,ba,b and cc satisfy the system of equations above, and a+b+ca+b+c is equal to xy \dfrac xy , where xx and yy are coprime positive integers, find x+yx+y.

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