Two systems of linear equations are said to be equivalent when they have exactly the same solutions. For instance

are equivalent, because we have just swapped the two first rows, and the requirements to fulfill are the same. On the other hand,

are equivalent too (and thus both systems have only one solution $(x=2,y=8,z=21)$), but this is not so obvious for the naked eye

Our strategy to solve systems of linear equations will be to get simpler and simpler equivalent systems, until we reach a system whose solutions are straightforward to find