A method and system for a turbofan gas turbine engine system is provided. The gas turbine engine system includes a variable pitch fan (VPF) assembly coupled to a first rotatable shaft and a low pressure compressor LPC coupled to a second rotatable shaft. The LPC including a plurality of variable pitch stator vanes interdigitated with rows of blades of a rotor of the LPC. The gas turbine engine system also includes a speed reduction device coupled to said first rotatable shaft and said second rotatable shaft. The gas turbine engine system further includes a modulating pressure relief valve positioned between an outlet of said LPC and a bypass duct and a controller configured to schedule a position of said plurality of variable pitch stator vanes and said modulating pressure relief valve in response to an operational state of said turbofan gas turbine engine system and a temperature associated with said LPC.