The open system elastic constants for a multicomponent alloy are derived and used to determine the equilibrium solute concentration profile surrounding an isolated coherent M2C carbide precipitate with a transformation strain with three unequal eigenstrains in an elastically anisotropic AF1410 steel. The open system bulk modulus was found to vary with stress in this alloy, indicating that the chemical thermodynamics of AF1410 in an open system can result in the material becoming nonlinearly elastic. However, the open system shear moduli are identical to their usual constant composition values as a result of the cubic symmetry of the solute expansion tensor. We find that the nonuniform stress field surrounding the misfitting precipitate will induce significant nonuniformities in the concentration of the chemical components in this alloy. At certain positions in the matrix, the change in the concentration of Cr and Mo due to the elastic stresses, relative to their average concentrations in the alloy, can be as large as 100 to 250 pct. Although the solute redistribution reduces the matrix effective bulk modulus by 12 pct, the coherent carbide elastic self-energy is reduced by only 0.45 pct, reflecting a large contribution of shear distortions to the elastic self-energy, which are relatively unaffected by the dilating solutes.