Merging two step functions while preserving all measurement points

Given are two step graphs representing the values of some quantity over time. Each graph is defined by a sorted array of pairs {coordinate, value}, where the coordinate is the point in time when a new step begins, and the value is maintained until the next coordinate. Before the first coordinate, the value is considered zero. The task is to construct a combined graph that contains all measurements from both original graphs, with the value at each point being the sum of the corresponding values from the first two graphs.

sum_series(first={{1, 2}, {5, 1}}, second={{2, 4}, {3, 6}, {9, 7}}) -> {{1, 2}, {2, 6}, {3, 8}, {5, 7}, {9, 8}}