This chapter introduces the method for solving a system of linear equations. The technique is used in many applications, including the popular input-output analysis (e.g., Hewings, 1985; see Appendix 11A for a brief introduction). Here, the method is illustrated in solving the Garin-Lowry model, a model widely used by urban planners and geographers for analyzing urban land use structure. A case study using a hypothetical city shows how the distributions of population and employment interact with each other and how the patterns can be affected by the transportation network. The GIS usage in the case study involves the computation of a travel time matrix and other data preparation tasks.