The two hybrid algorithms Sumudu HPM and Elzaki HPM are used in the current study to tackle coupled Burgers' equations and produce accurate results. To demonstrate the validity of the given approaches, three instances are used. Applying Sumudu HPM and Elzaki HPM yields the same approximate and exact answers in all of the examples taken into consideration, which is proved with the help of the accompanying figures. It attests to the entire acceptance and accuracy of the solutions produced by these methods. The proposed regimes also have error and convergence analyses available. The current analytical regimes offer a more effective method of handling partial differential equations than the intricate numerical systems. It is also asserted that exact and approximation solutions are compatible. Also announced is the planned regime's numerical convergence.