Hopefully I have this in the right place, it's not a homework question exactly, rather a question I have as I'm reading through my text. I'm learning about free variables. The book gives the example system: x - z = 2 y + 2z = -1 0 = 0 as an example of a system with infinitely many solutions. I see that the way to express the solution set for this system is by describing the line that the solutions lie on. It says to make z the 'free variable' and make x and y the 'dependent' variables. Then by picking z I can find values for x and y that work. This makes sense to me. But why can't I solve for, say, x and z in terms of y? Why do I have to pick z as the free variable?