Question 144314
it is a well known postulate that two lines always meet at only one point.there can not be more than one point where two lines can intersect.
Now consider the following system of linear equations
                         a*x+b*y=c ......(1)
                         g*x+f*y=d ........(2)
  let they both intersect at two distinct points say (x1,y1) and (x2,y2)
  then we will have
                        a*x1+b*y1=c               a*x2+b*y2=c
                        g*x1+f*y1=d   and         g*x2+f*y2=d
so a*x1+b*y1=a*x2+b*y2  :::> a*(x1-x2)=b*(y2-y1)
similarly from others        g*(x1-x2)=f*(y2-y1)
by dividing these equations we get a/g=b/f which can not be possible because lines are not parallel according to our supposition.hence 
                         x1-x2=0 and y2-y1=0
                            x1=x2 and y1=y2 
which prove that points are not distinct .