In this paper a combined optimization of a coupled electricity and gas system is presented. For the electricity network a unit commitment problem with optimization of energy and reserves under a power pool, considering all system operational and unit technical constraints is solved. The gas network subproblem is a medium-scale mixed-integer nonconvex and nonlinear programming problem. The coupling constraints between the two networks are nonlinear as well. The resulting mixed-integer nonlinear program is linearized with the extended incremental method and an outer approximation technique. The resulting model is evaluated using the Greek power and gas system comprising fourteen gas-fired units under four different approximation accuracy levels. The results indicate the efficiency of the proposed mixedinteger linear program model and the interplay between computational requirements and accuracy.