cant we say that for lambda=1 we have endless solutions?
but also we can divide equation 2 and 3 by lambda-1 and after that so for lambda=1 we get that there is no solutions
so what is the correct solution
Which corresponds to the equations x+ y+ z= 1, 0= 0, 0= 0. It should be obvious that you can choose, say, y and z to be any numbers you want and solve for the corresponding x. That is why there are an infinite number of solutions.
As HappyJoe said (may he long be happy), you can only divide by as long as so that it is not valid to do that and then let .