This dissertation is based on the magnetotransport study of the 2DES in GaAs/AlGaAs heterostructure. There are two separate studies presented in this dissertation. The first study focuses on the study of the microwave induced resistance oscillations in presence of supplementary direct current ( I_DC). Our works find that the peak height of the microwave induced magnetoresistance oscillations in high mobility GaAs/AlGaAs two-dimensional electron system (2DES) are progressively reduced by applied direct current ,I_DC, over the temperature range 0.35K – 1.25K and I_DC also produces an overall giant magnetoresistance. A “universality” or similarity in the decay of the magnetoresistance peak height across varying temperatures T, channel width W and applied I_DCwas observed. The results suggest that the resistance maxima scale with current densityj_DC=I_DC/W rather than the I_DC and indicate that the bulk current is maintained at the photo-excited magnetoresistance peaks in the photo-excited 2DES. On the other hand, the oscillatory minima show limited sensitivity to I_DC . The second study focuses on the mutual influence between current induced giant magnetoresistance (GMR) and the microwave radiation induced oscillations in various temperatures. This study demonstrates that a dc-current, I_DC,tunable giant magnetoresistance can exist together with radiation-induced magnetoresistance oscillations in the GaAs/AlGaAs two-dimensional electron system. Both effects are decoupled and can be separated in a Drude multi-conduction model. The result suggests that the introduced I_DC, reduces the overall diagonal conductivity, diminishes and eventually eliminates the conductivity peaks at the oscillatory maxima. This behavior, captured using a two-term Drude model, shows that the fit parameter σ_1 decreases with increasing I_DC, even reversing sign, indicating a transition from positive to negative magnetoresistance. The crossover current increases with temperature. At high I_DC, σ_1 shifts from negative to positive as temperature rises from 0.35 K to 1.25 K, suggesting temperature-dependent reversal of negative magnetoresistance.