We study the $J/ψ\to γπ^+ π^-$, $γπ^0 η$ reactions from the perspective that they come from the $J/ψ\to ϕ(ω) π^+ π^-, ρ^0π^0 η$ reactions, where the $ρ^0$, $ω$, and $ϕ$ get converted into a photon via vector meson dominance. Using models successfully used previously to study the $J/ψ\to ω(ϕ) ππ$ reactions, we make determinations of the invariant mass distributions for $π^+ π^-$ in the regions of the $f_0(500)$, $f_0(980)$, and for $π^0 η$ 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.

14 pages, 9 figures