Find a+b+c, given that \(\begin{align*} ax+by+c&=x+7,\\ a+bx+cy&=2x+6y,\\ ay+b+cx&=4x+y. \end{align*}\)
Adding gives
\((a + b + c)(1 + x + y) = 7(1 + x + y)\)
which means a + b + c = 7 if \(x + y \neq -1\).
(The formula is easily verifiable by expanding the terms and comparing to what you have after adding the three equations.)
Thanks!
+865 
