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This study investigates the constraint provided by greenhouse gas measurements from space on surface fluxes. Imperfect knowledge of the light path through the atmosphere, arising from scattering by clouds and aerosols, can heavily bias column measurements retrieved from space. To minimize the impact of such biases, ratios of total column retrieved CH4 and CO2 (Xratio) have been used. We apply the ratio inversion method described in Pandey et al. (2015) to retrievals from the Greenhouse Gas Observing SATellite (GOSAT). The ratio inversion method uses the measured Xratio as a weak constraint on CO2 fluxes. In contrast, the more common approach of inverting proxy CH4 retrievals (Frankenberg et al., 2005) prescribes atmospheric CO2 fields and optimizes only CH4 fluxes. The TM5-4DVAR inverse modeling system is used to simultaneously optimize the fluxes of CH4 and CO2 for 2009 and 2010. The results are compared to proxy inversions using model-derived-XCO2 mixing ratios (XCO2model) from CarbonTracker and MACC. The performance of the inverse models is evaluated using aircraft measurements from the HIPPO, CONTRAIL and AMAZONICA projects. Xratio and XCO2model are compared with TCCON retrievals to quantify the relative importance of errors in these components of the proxy XCH4 retrieval (XCH4proxy). We find that the retrieval errors in Xratio (mean = 0.61 %) are generally larger than the errors in XCO2model (mean = 0.24 % and 0.01 % for CarbonTracker and MACC, respectively). On the annual time scale, the CH4 fluxes from the different satellite inversions are generally in agreement with each other, suggesting that errors in XCO2model do not limit the overall accuracy of the CH4 flux estimates. On the seasonal time scale, however, larger differences are found due to uncertainties in XCO2model, particularly over Australia and in the tropics. The ratio method stays closer to the a priori CH4 flux in these regions, because it is capable of simultaneously adjusting the CO2 fluxes. Over Tropical South America, comparison to independent measurements shows that CO2 fields derived from the ratio method are less realistic than those used in the proxy method. However, the CH4 fluxes are more realistic, because the impact of unaccounted systematic uncertainties is more evenly distributed between CO2 and CH4. The ratio inversion estimates an enhanced CO2 release from Tropical South America during the dry season of 2010, which is in accordance with the findings of Gatti et al. (2014) and Vanderlaan et al. (2015). The performance of the ratio method is encouraging, because despite the added non-linearity due to the assimilation of Xratio and the significant increase in the degree of freedom by optimizing CO2 fluxes, still consistent results are obtained.