If that were correct or you after you reduce it correctly, to get something like "z= a value" you have to divide by the coefficient of z. You cannot do that is a is such that the coefficient is 0. For one value of a, you will get something like 0z= 0, so that z can be anything and there are an infinite number of solutions, while for another you get something like 0z= 7 which is not true for any z- there is no solution. Notice, by the way, that you are NOT required to find the solution in the case that there is a unique solution. That simplifies the arithmetic! Also, although it says "solution space", this is not a homogeneous system and so the solution set is not a subspace.