Through the use of the well-known holograph transformations (based on the inversion of the role of dependent and independent variables), a class of non-linear systems represented by a pair of coupled second-order partial differential equations is shown to be reducible to a pair of uncoupled linear systems described by Laplace equations. The inverse functions of the solutions to these Laplace equations represent the solutions of the original equations. Thus, in some sense, the coupled equations representing the given non-linear system can be considered as ’ inverse ’ Laplace equations. It is observed that the hodograph transformation in effect is a decoupling technique ; and, in addition, leads to equivalent linear systems for the class of systems considered.