Suppose that the three lines ax+by=c, (a+2)x+(b-3)y=c+9, and (a+1)x+(b-1)y=c+2 are concurrent at point M. What is the sum of coordinates M?

Answer 1

ax + 2x + by - 3y = c + 9; 2x - 3y = 9; ax + x + by - y = c + 2; x - y = 2; x = 2 + y; 4 + 2y - 3y = 9; y = - 5;

x = - 3; (x + y) = - 8