The 13 single-crystal adiabatic elastic moduli (Cij) of a C2/c jadeite sample close to the ideal composition (NaAlSi2O6) and a natural P2/n diopside-rich omphacite sample have been measured at ambient condition by Brillouin spectroscopy. The obtained Cij values for the jadeite sample are: C11 = 265.4(9) GPa, C22 = 247(1) GPa, C33 = 274(1) GPa, C44 = 85.8(7) GPa, C55 = 69.3(5) GPa, C66 = 93.0(7) GPa, C12 = 84(1) GPa, C13 = 66(1) GPa, C23 = 87(2) GPa, C15 = 5.4(7) GPa, C25 = 17(1) GPa, C35 = 28.7(6) GPa, C46 = 14.6(6) GPa. Voigt-Reuss-Hill averaging of the Cij values yields aggregate bulk modulus KS = 138(3) GPa and shear modulus G = 84(2) GPa for jadeite. Systematic analysis combing previous single-crystal elasticity measurements within the diopside-jadeite solid solution indicates that the linear trends are valid for most Cij values. The νp and νs of omphacite decrease with diopside content, though the velocity changes are small as diopside component exceeds 70%. We also found that both the isotropic νp and νs, as well as the seismic anisotropy of eclogite, changed strongly with the bulk-chemical composition. The relationship between the anisotropic velocities of eclogite and the chemical composition can be a useful tool to trace the origin of the eclogitic materials in the Earth's mantle.