1. The problem statement, all variables and given/known data Show that elementary row operations don't affect solutions sets in linear systems 2. Relevant equations - 3. The attempt at a solution It's pretty easy to come up with a random linear system and perform ERO on them and showing that solutions are not affected, but is there all there is to it? Do I need to show that this works throughout all possible forms of linear systems or will this be known as "proving"?