Existence and uniqueness of solutions to systems of delay dynamic equations on time scales

The purpose of this paper is to establish Picard-Lindel"{o}f theorem for local uniqueness and existence results for first-order systems of nonlinear delay dynamic equations. In the linear case, we extend our results to global existence and uniqueness of solutions on the entire interval (allowed to be unbounded above), and prove the variation of parameters formula for the unique solution in terms of the principal solution. A simple example concerning the ordinary case is also provided.