Do you see a pattern

Algebra Level 3

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

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