Do you see a pattern

Algebra Level 3

a+4b+9c=34a+9b+16c=59a+16b+25c=7\begin{aligned} a + 4b + 9c &= 3 \\ 4a + 9b + 16c &= 5 \\ 9a + 16b + 25c &= 7 \\ \end{aligned}

If a,b,ca,b,c are real numbers satisfying the above system, determine the value of a+b+ca+b+c.

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