Quasielastic scattering angular distributions have been measured for the ⁷Be  + ⁹Be  system at E_lab = 17, 19 and 21 MeV in the angular range q_cm = 24°  57°. An optical model (OM) analysis of these data has been carried out in order to extract optical potential parameters and reaction cross-sections. One-proton stripping cross-sections were also measured for this system at E_lab = 19 and 21 MeV. These transfer angular-distribution data were compared with the finite-range distorted-wave Born approximation (FRDWBA) calculations. For the ⁷Li + ⁹Be system quasielastic scattering angular distributions were measured and emitted light charged particles were detected at E_lab = 15.75, 24.00 and 30.00MeV in the angular range  q_cm = 7°  70° . Fusion cross-sections were obtained by reproducing the measured a-evaporation spectra from the compound nucleus at backward angles with the statistical model calculations. The ratios of the experimental fusion cross-sections to the total reaction cross-sections (obtained from OM analysis) were found to be small. This result suggests that the break-up process has a strong influence on the fusion process leading to a reduction in the fusion cross-section.