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.
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