In recent papers, both Robinson and the author have considered the behavior of the solution set of systems of linear equalities and inequalities where the vectors and matrices defining the set are subjected to perturbations. Robinson’s aim has been to identify special conditions on the systems so that the solution sets will be stable under arbitrary perturbations, while the author’s goal has been to identify special perturbations under which arbitrary systems will be stable. In this brief note we relate the two viewpoints by showing the more fundamental nature of Robinson’s results, deriving both types of conditions from one simple special case of the Robinson analysis.