Dry reforming of methane (DRM) is a promising technology to convert carbon dioxide (CO2) and methane (CH4), two major greenhouse gases into syngas (a mixture of carbon monoxide (CO) and hydrogen (H2)). A thermodynamic equilibrium analysis for DRM with a focus on carbon formation is carried out in Aspen Plus using the Gibbs free energy minimization method. The effects of feed CO2/CH4 ratio (0.5–3), reaction temperature (773–1373 K), and system pressure (0.1–10 atm) on the equilibrium conversion, product distribution, and solid carbon formation are investigated. From the analysis, it was found that the optimal operating conditions of 1 atm, 1123 K, and a feed ratio (CO2:CH4) of 1:1, minimized carbon formation, produced syngas at a H2/CO ratio of 1 (sufficient for downstream Fischer–Tropsch synthesis), while minimizing energy requirements. It is found that adding small amounts of oxygen or water significantly reduced carbon formation, minimized loss in syngas production, and reduced energy requirements. Three application scenarios were simulated to reflect the valorization of vented and flared natural gas and landfill gas (LFG). It was found that using captured CO2 with natural gas and LFG produced favorable results and therefore may be an opportunity for commercial DRM.