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{5a+3b+c=171a+4b+7c=21\large{ \begin{cases} 5a+3b+c=17 \\ 1a + 4b+7c=21 \end{cases}} ⎩⎨⎧5a+3b+c=171a+4b+7c=21
Given that a,ba,ba,b and ccc satisfy the system of equations above, and a+b+ca+b+ca+b+c is equal to xy \dfrac xy yx, where xxx and yyy are coprime positive integers, find x+yx+yx+y.
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