Behavioral studies have long shown that humans solve problems in two ways, one intuitive and fast (System 1, model-free), and the other reflective and slow (System 2, model-based). The neurobiological basis of dual process problem solving remains unknown due to challenges of separating activation in concurrent systems. We present a novel neuroeconomic task that predicts distinct subjective valuation and updating signals corresponding to these two systems. We found two concurrent value signals in human prefrontal cortex: a System 1 model-free reinforcement signal and a System 2 model-based Bayesian signal. We also found a System 1 updating signal in striatal areas and a System 2 updating signal in lateral prefrontal cortex. Further, signals in prefrontal cortex preceded choices that are optimal according to either updating principle, while signals in anterior cingulate cortex and globus pallidus preceded deviations from optimal choice for reinforcement learning. These deviations tended to occur when uncertainty regarding optimal values was highest, suggesting that disagreement between dual systems is mediated by uncertainty rather than conflict, confirming recent theoretical proposals.