As other comments note, this is not the definition of a linear system. However, it is the definition of a time-invariant system, which is probably why it's comi

As other comments note, this is not the definition of a linear system. However, it is the definition of a time-invariant system, which is probably why it's coming to mind here. Systems that are both linear and time-invariant, sometimes abbreviated to LTI systems, are the most common sort of thing (i.e., model) that one actually analyzes. When time-dependence is present, it is always modelled explicitly and usually modelled as a complication of a time-invariant system.