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:(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Quick question about free variables

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