This paper investigates the distributed optimal coordination (DOC) problem for multiple heterogeneous linear systems over strongly connected communication networks. By exploiting output regulation techniques, constructing a Laplacian matrix based on the outdegree, and assigning each agent an additional scalar state variable, a new DOC algorithms is developed, which can solve the DOC problem using the outdegree information of all agents. In contrast to the existing results, this paper presents a new technique to solve the DOC problem for multiple heterogeneous linear systems over weighted-unbalanced communication networks. Finally, numerical simulations are presented to illustrate the effectiveness of the designed algorithm.