Abstract: We study the J/psi -> gamma pi(+)pi(-), gamma pi(0)eta reactions from the perspective that they come from the J/psi -> phi(omega)pi(+)pi(-), rho(0)pi(0)eta reactions, where the rho(0), psi, and phi get converted into a photon via vector meson dominance. Using models successfully used previously to study the J/psi -> omega(phi)pi pi reactions, we make determinations of the invariant mass distributions for pi(+)pi(-) in the regions of the f(0)(500), f(0)(980), and for pi(0)eta in the region of the a(0)(980). The integrated differential widths lead to branching ratios below present upper bounds, but they are sufficiently large for future check in updated facilities.