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The progenitor systems and explosion mechanism of Type Ia supernovae are still unknown. Currently favoured progenitors include double-degenerate systems consisting of two carbon-oxygen white dwarfs with thin helium shells. In the double-detonation scenario, violent accretion leads to a helium detonation on the more massive primary white dwarf that turns into a carbon detonation in its core and explodes it. We investigate the fate of the secondary white dwarf, focusing on changes of the ejecta and observables of the explosion if the secondary explodes as well rather than survives. We simulate a binary system of a $1.05\,\mathrm{M_\odot}$ and a $0.7\,\mathrm{M_\odot}$ carbon-oxygen white dwarf with $0.03\,\mathrm{M_\odot}$ helium shells each. We follow the system self-consistently from inspiral to ignition, through the explosion, to synthetic observables. We confirm that the primary white dwarf explodes self-consistently. The helium detonation around the secondary white dwarf, however, fails to ignite a carbon detonation. We restart the simulation igniting the carbon detonation in the secondary white dwarf by hand and compare the ejecta and observables of both explosions. We find that the outer ejecta at $v~>~15\,000$\,km\,s$^{-1}$ are indistinguishable. Light curves and spectra are very similar until $\sim~40\,\mathrm{d}$ after explosion and the ejecta are much more spherical than violent merger models. The inner ejecta differ significantly slowing down the decline rate of the bolometric light curve after maximum of the model with a secondary explosion by $\sim20$ per cent. We expect future synthetic 3D nebular spectra to confirm or rule out either model.