Find a+b+c, given that ax+by+c=x+7,a+bx+cy=2x+6y,ay+b+cx=4x+y.
Adding gives
(a+b+c)(1+x+y)=7(1+x+y)
which means a + b + c = 7 if x+y≠−1.
(The formula is easily verifiable by expanding the terms and comparing to what you have after adding the three equations.)
Thanks!