1. The problem statement, all variables and given/known data I just don't understand how one chooses a free variable when using Gaussian elimination and back substitution to solve linear equations 2. Relevant equations 3. The attempt at a solution One particular example here is provided (already in row echelon form) -2 -2 0  0 0 0 0  0 0 0 0  0 The free variables to this particular example is x_2 and x_3. I'm lost what method does one use to arrive to this conclusion? Thanks for the help.