  The optical spectra of Seyfert galaxies are often dominated by emission lines
excited by both star formation and AGN activity. Standard calibrations (such as
for the star formation rate) are not applicable to such composite (mixed)
spectra. In this paper, we describe how integral field data can be used to
spectrally and spatially separate emission associated with star formation from
emission associated with accretion onto an active galactic nucleus (AGN). We
demonstrate our method using integral field data for two AGN host galaxies (NGC
5728 and NGC 7679) from the Siding Spring Southern Seyfert Spectroscopic
Snapshot Survey (S7). The spectra of NGC 5728 and NGC 7679 form clear sequences
of AGN fraction on standard emission line ratio diagnostic diagrams. We show
that the emission line luminosities of the majority (> 85 per cent) of spectra
along each AGN fraction sequence can be reproduced by linear superpositions of
the emission line luminosities of one AGN dominated spectrum and one star
formation dominated spectrum. We separate the Halpha, Hbeta, [N
II]$\lambda$6583, [S II]$\lambda \lambda$6716, 6731, [O III]$\lambda$5007 and
[O II]$\lambda \lambda$3726, 3729 luminosities of every spaxel into
contributions from star formation and AGN activity. The decomposed emission
line images are used to derive the star formation rates and AGN bolometric
luminosities for NGC 5728 and NGC 7679. Our calculated values are mostly
consistent with independent estimates from data at other wavelengths. The
recovered star forming and AGN components also have distinct spatial
distributions which trace structures seen in high resolution imaging of the
galaxies, providing independent confirmation that our decomposition has been
successful.
