From a viewpoint of water polyamorphism, we examined the states of solvent water in the glassy dilute LiCl-water solutions and in the glassy dilute glycerol-water solutions and studied the effects of the solute on the polyamorphic behaviors of the solvent water. The states of the glassy solvent water are able to be characterized by the states of low- and high-density amorphous ices, LDA and HDA, respectively. The polyamorphic transition of aqueous solution depends on the solute concentration and the solute component. There exists a region in which LDA-like solvent water and HDA-like solvent water coexist in the pressure-temperature-concentration diagram of aqueous solution. The extent of the coexistence region seems to relate to the difference between the solubility of solute in the two kinds of solvent water. The behaviors of glassy aqueous solution are consistent with the water polyamorphism. This result provides insight not only into the relation between the hydration and the two kinds of water but also into the dynamics of macromolecules surrounded by water.