The rapid spread of antibiotic-resistant pathogens has prompted drug combinations to maintain clinical efficacy and combat the development of resistance. Drugs interact to increase (synergistic) or decrease (antagonistic) the effect of the combined therapy. Furthermore, the interactions of the two drugs can change as the bacteria evolves from the wild type (WT) to the mutant type (MT). Experimental studies have shown that the evolution of resistance is impeded if drugs interact antagonistically in the WT. In contrast, other studies have shown that antagonistic interactions in the MT speed up the resistance's emergence. Theoretical works investigated the effect of WT drug interactions on resistance. A fundamental question is how the different combination of drug interactions in WT and the MT influences antimicrobial resistance. Here we analyze a mathematical model that captures any combination of drug interactions in WT and the MT. The novelty of this work is to examine the association between synergistic and antagonistic interaction of antibiotics for wild-type (sensitive bacteria) and mutants (resistant bacteria) on the growth rate of resistant strains. The most important contribution is to clarify that antagonistic interaction against the wild type has a more critical role in slowing the growth rate of resistant bacteria. The antagonistic interaction in the MT speeds up evolution but minimally. Our results suggest that it would be more appropriate to consider the nature of the drug interactions for the WT when designing combination therapy.