In some specific cases, boundary value problems provide a dual solution in which one solution is physically reliable and stable whereas the other solution is unstable. This work is performed to express the dual solutions of Ag-MgO/water hybrid nanofluid flow over an extending/contracting Riga wedge and stagnation point. Two solutions are obtained for a limited range of extending/contracting parameter and suction/injection parameter. The detailed stability test is carried out to determine which of the two solutions is physically reliable and stable. Suitable self-similarity variables are employed to convert the fluid transport equations into ordinary differential equations, which have been computed by using the bvp4c in MATLAB. The impacts of active parameters on flow field are illustrated graphically. The outcome of the present result reveals that the suction/injection parameter enhances the skin friction at the Riga wedge and stagnation point for the first solution, while the opposite behavior is observed for the second solution. It is noticed that the critical values increase for the given values of Ag-MgO nanoparticles volume fraction on rate of heat transfer. The modified Hartmann number lowers the temperature for the first solution over a wedge and stagnation point. The stability test reveals that the first solution is stable. © 2020 by Begell House, Inc. www.begellhouse.com.