Our proof of the Strong Duality Theorem, as well as the presentation of the tableau method in Section 3, depended on the fact that the dictionary and tableau methods were equivalent. More specifically, solving for an entering basic variable in a constraint equation, and then substituting the resulting expression into all other equations, is equivalent to pivoting about the element in the row of the departing basic variable and the column of the entering basic variable in the related simplex tableau. Consider a general standard maximum problem in equality form, and show for the first step of the algorithm that this is indeed the case.