Angular distributions have been measured for the reactions ⁹⁰Zr(⁶Li,⁷Be_GS)⁸⁹Y, ⁹⁰Zr(⁶Li,⁷Be_0.43)⁸⁹Y, ⁸⁹Y(⁶Li,⁷Be_GS)⁸⁸Sr and ⁸⁹Y(⁶Li,⁷Be_0.43)⁸⁸Sr at an incident beam energy of 60 MeV in the angular range 6 degrees -45 degrees (lab). Exact finite-range distorted-wave Born approximation calculations have been performed and were found to be moderately successful in reproducing the shape of the experimental angular distribution. The optical-model parameters used in the calculations were obtained from a global set of parameters which was capable of reproducing the ⁶Li and ⁷Li elastic scattering data taken at 60 MeV. In the analysis of the reaction data the ⁷Be_GS was assumed to be a mixed state of 1p_3/2 and 1p_1/2 configurations, whilst the ⁷Be_0.43 state was assumed to be due to a pure 1p_3/2 configuration, in agreement with shell-model calculations and previous experimental results. Spectroscopic factors were deduced from a comparison of the theoretical and experimental cross sections. The results obtained were found to be in good agreement with those deduced from light-ion reactions.