This paper presents some theoretical findings from our recent methodological research addressing the issue of variable elimination by equality edit in linear editing. The research was motivated by seeking improvement of computational efficiency for error localization, when implementing an error localization module for the editing and imputation of NASS’ large surveys. Our results, extending some of Fellegi and Holt (1976) results on linear edits, establish the method of elimination by equality edit in linear editing, which leads to a simplified linear editing problem in reduced dimension. The methodological establishment of this paper can be particularly useful as applied to the U.S. Census of Agriculture editing and imputation, for which a considerable number of the linear edits are equality ones. It is expected that the implementation of this methodology, in conjunction with other computational improvements, may enable Fellegi-Holt methodology to be implemented into the editing systems for future censuses and sample surveys with improved efficiency and accuracy.