How to minimize the emission of air pollutants while making decisions about mitigating climate change has become a hot research topic. Considering the homologous homology of the two types of emissions, it is completely feasible to achieve synergistic control for different pollutants through a rational allocation of technology investment. To attain this goal, in this paper, I propose a pollutant synergistic control model. Carbon and sulfur emissions are chose as the major control object. Under a weak condition, I obtained analytical expressions for two types of cleaner technology investment paths, technology capital accumulation paths, and emission reduction paths. Further, characteristics of the respective paths, and the conditions for meeting the corresponding theoretical inflection points or peaks, were analyzed, which lays a foundation for applications of the theory. In particular, this study draws the necessary and sufficient conditions for an internal solution to the choice of cleaner technology, which is a powerful and practical evaluation index. The theoretical predictions were verified with numerical simulation. The investment of the two types of cleaner technologies peaked during the 10th period, and the capital accumulation peaked during 15th period after a slight delay. The actual measured investment and subsidy feedback gains were around the 0.04 and 0.02 levels. In addition, different combinations of targets for sulfur and carbon reduction also simulated scenarios in which the model had different internal solutions. The relevant theoretical exploration work in this paper has deep implications for policy decisions in the real world.