Existence of coupled Kahler-Einstein metrics using the continuity method

In this paper, we prove the existence of coupled Kahler-Einstein metrics on complex manifolds whose canonical bundle is ample. These metrics were introduced and their existence in the said case was proven by Hultgren and Nystrom using calculus of variations. We prove the result using the method of continuity. In the process of proving estimates, akin to the usual Kahler-Einstein metrics, we reduce existence in the Fano case to a C-0 estimate.