This article introduces a novel notion concerning a system of homogeneous difference equations (^E): a P-Self-Semi-Homogeneous System (PSSHS) of order m, denoting a positive integer for both p and m. The article differentiates between two states (p=1 and p≠1, respectively) and two substrates (m=1 and m≥2), where m represents a value for each state. A matrix containing coefficients of the identical dimension (2×2) was used to summarize the work. The argument is substantiated by a compilation of definitions, findings, evidence that constitute the body of our article. In conclusion, instances and resolutions for every scenario are presented, each of which can be resolved through one of three distinct methods: application of the definition, application of the result, or utilization of the theorem.