The straight lines 4ax + 3by + c = 0, where a + b + c = 0, are concurrent at the point

The set of lines is 4ax + 3by + c =  0, where a + b + c = 0. Eliminating c, we get 4ax+3by−(a+b)=0 or  a(4x−1)+b(3y−1)=0This passes through the intersection of the lines 4x - 1 = 0  and 3y−1=0 , i.e., x=1/4,y=1/3 , i.e., (1/4,1/3) .