Real numbers $a$, $b$, $c$, $x$, and $y$ satisfy \begin{align*} ax+by+c&=x+7,\\ a+bx+cy&=2x+6y-4,\\ ay+b+cx&=8x+5y-3, \end{align*} and $x + y \neq -1$. Find $a+b+c$.
\( $x + y \neq -1$ \)
Add the equations
a ( x + y) + a + b(x + y) + b + c (x + y) + c = 11x + 11y
(a + b + c) + (x + y) (a + b + c) = 11 ( x + y)
(a + b + c) (x + y + 1) = 11 (x + y)
a + b + c = 11 (x + y) / ( x + y + 1)
+1911 
