The potential of hybrid nanofluid as an alternative heat transfer fluid is undoubted and the insightful research on enhancing its thermal conductivity is crucial. This study accentuates the influence of magnetic field and thermal radiation on the ethylene glycol base hybrid nanofluid with a combination of argentum and magnetite nanoparticles. The mathematical equations of the hybrid nanofluid model are derived with the suitable similarity transformations and then solved numerically with the execution of bvp4c codes in Matlab software. Graphical results show that an upsurge in magnetic parameter reduces the momentum boundary layer thickness while the higher thermal radiation enlarges the thermal boundary layer thickness. The effects of suction and nanoparticles concentration are also presented graphically. Stability analysis reveals that the first solution obtained in this study is stable, and conversely, the second solution is not.