If the lines (A1)X + (B1)Y + (c1) = 0 and (A2)X + (B2)Y + (C2) = 0 are not parallel and K is any constant, show that :

((A1)X + (B1)Y + (c1)) + K((A2)X + (B2)Y + (C2)) = 0

Is a line throught the point of intersection of the given lines. When K is assigned various values, this equaion represents various members of the family of all lines through the point of intersection.

Can anyone give me any tips to solving this one ? I tried alot last night but couldnt figure it out. How Do I show that its true anyway? Plus you cant even add them together since there in parenthesies right? What should I do?