The main purpose of this approach is to convert linear equations into linear equations and find an algebraic solution. This research is a library research, reliable internal and external sources have been used for data collection. After an in-depth investigation and comparison, the findings indicated that the calculations are done simply with the help of the algebraic algorithm. It is because algebraic concepts are used in calculations and understanding algebraic concepts is very easy for every student. Several obvious examples have been brought to emphasize the effectiveness of the linear equation solving strategy. The work of the above algorithm in the field of encryption is explained in the framework of the RSA encryption system, which shows the effect of the algebraic algorithm.