This is not a homework question. But a question on how to understand what my textbook does. It is about choosing the free variables. Let's say I have the system of equations: x1-2x2+3x3+2x4+x5 =10 x3 +2x5=-3 x4 -4x5=7 Then my book says that we choose x2 and x5 to be free variables, since they are not leading. And we set x2=t and x4=s and solve the system. But why do we have to choose x2 and x5 just because they are not leading? I mean, Can't I say x2=t and x5=s instead of x4?