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 $x+y$ .