Dictionary:Back substitution

{{#category_index:B|back substitution}} When simultaneous equations can be expressed as $A\cdot X=B$, where $A$ is a triangular matrix and $X$ and $B$ are vectors, the solution for the last (or first) value becomes trivial. Back-substitution then involves successively replacing the last (or first) value in the equations for the other elements so that their solutions also become trivial.