The effects of solid solution on the deformation behavior of binary Mg–xZn (x = 0, 1, 2 wt%) alloys featuring a designated texture that enables extension twinning under tension parallel to the basal pole in most grains, were investigated using in-situ neutron diffraction and the EVPSC-TDT model. Neutron diffraction was used to quantitatively track grain-level lattice strains and diffraction intensity changes (related to mechanical twinning) in differently oriented grains of each alloy during cyclic tensile/compressive loadings. These measurements were accurately captured by the model. The stress-strain curves of Mg-1 wt%Zn and Mg-2 wt%Zn alloys show as-expected solid solution strengthening from the addition of Zn compared to pure Mg. The macroscopic yielding and hardening behaviors are explained by alternating slip and twinning modes as calculated by the model. The solid solution’s influence on individual deformation modes, including basal 〈a〉 slip, prismatic 〈a〉 slip, and extension twinning, was then quantitatively assessed in terms of activity, yielding behavior, and hardening response by combining neutron diffraction results with crystal plasticity predictions. The Mg-1 wt%Zn alloy displays distinct yielding and hardening behavior due to solid solution softening of prismatic 〈a〉 slip. Additionally, the dependence of extension twinning, in terms of the twinning volume fraction, on Zn content exhibits opposite trends under tensile and compressive loadings.