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In this paper, we consider exact solutions of Maccari system. We tackle extended trial equation method and generalized Kudryashov method to find exact solutions of this system. Initially, we obtain some exact solutions such as rational function solution, travelling wave solution, soliton solution, Jacobi elliptic function solution, hyperbolic function solution and periodic wave solution of this system by using extended trial equation method. Also, we attain dark soliton solutions of this system by using generalized Kudryashov method. Finally, for suitable parameter values, we plot two and three dimensional graphics of imaginary and real values of some exact solutions that we found by using both methods. [ABSTRACT FROM AUTHOR]