Stabilizing a flame in scramjet engines is a current technological challenge. Indeed, the residence time in the combustion chamber is very short, thus limiting the mixing efficiency and consequently, the combustion. This problem is presently addressed by simulating the scramjet combustor of the U.S Air Force Research Laboratory in which ethylene is injected from the back of a slanted cavity to react with the supersonic airflow. Large-Eddy Simulations (LES) are performed for different cases showing a dependence of the combustion regimes encountered in the scramjet cavity with the fuel flow rate. For a medium-high flow rate, a mix of lean and rich premixed reaction zones is found along with non-premixed flames. At medium flow rate, rich premixed flames disappear but the flame remains stable in the cavity. The mechanism of flame stabilization is detailed and the LES tool has proven its efficiency in such challenging configuration. Finally, a mechanism of extinction is proposed when the fuel flow rate is further reduced.