A system for supplying a working fluid to a combustor includes a fuel nozzle, a combustion chamber downstream from the fuel nozzle, and a flow sleeve that circumferentially surrounds the combustion chamber. Injectors circumferentially arranged around the flow sleeve provide fluid communication through the flow sleeve and into the combustion chamber. A valve upstream from the injectors has a first position that permits working fluid flow to the injectors and a second position that prevents working fluid flow to the injectors. A method for supplying a working fluid to a combustor includes flowing a working fluid through a combustion chamber, diverting a portion of the working fluid through injectors circumferentially arranged around the combustion chamber, and operating a valve upstream from the injectors to control the working fluid flow through the injectors.