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When the question is asking about favorability, it is really asking about the magnitude of the Gibb's free energy. The more negative this value, the more favorable a reaction is. Gibb's depends on enthalpy and a temperature scaled entropy: (G=H-T*S). When we think of nucleophilic elimination, we know that a Hydrogen atom is removed by a nucleophilic group resulting in our final product. Since a Hydrogen is removed in elimination, while left intact during substitution, there are more final species formed during an elimination reaction. According to general chemistry principles, this means that there was a larger increase in entropy compared to the substitution. As temperature increases this larger entropy becomes more noticeable as it is now scaled by a larger T. Therefore at low temperature, the enthalpy term dominates Gibbs and the substitution reaction prevails. However as T grows, so does the entropy term and at high T this overrides enthalpy, making the elimination reaction more favorable.