This study addresses the urgent need to reduce carbon emissions in the power sector, a major contributor to global greenhouse gas emissions, by employing system engineering principles coupled with machine learning techniques. It focuses on analyzing the interplay between regional marginal prices (LMP) and carbon emissions within electricity markets. Leveraging a dataset that encompasses hourly LMP and carbon emissions data across various regions of New York State, the paper explores how market designs and operational strategies influence carbon output. The analysis utilizes neural networks to simulate and predict the effects of different market scenarios on carbon emissions, highlighting the role of LMP, loss costs, and congestion costs in environmental policy effectiveness. The results underscore the potential of system engineering to provide a holistic framework that integrates market dynamics, policy adjustments, and environmental impacts, thereby offering actionable insights into optimizing market designs for reduced carbon footprints. This approach not only enhances the understanding of the complex interactions within electricity markets but also supports the development of targeted strategies for achieving sustainable energy transitions.