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In this paper, we solve the simultaneous Diophantine equationsm.(x_1^k+....+x_{t_1}^k)=n.(y_1^k+....+y_{t_2}^k); k=1,3, where t_1, t_2>3, andm, n are fixed arbitrary and relatively prime positive integers. This is doneby choosing two appropriate trivial parametric solutions and obtaininginfinitely many nontrivial parametric solutions. Also we work out someexamples, in particular the Diophantine systems of A^k+B^k+C^k=D^k+E^4; k=1,3.

On the simultaneous Diophantine equations m.(x_1^k+....+x_{t_1}^k)=n.(y_1^k+....+y_{t_2}^k); k=1,3