Is my HVAC system one or two transformer based?

Question

I have read Do I have one or two 24V transformers in HVAC control circuit, but as it appears I don't have two geographically separate units for A/C and heating, believe this to be a different question.

However I also bought the Nest E for installation, and hence need to know if this one transformer thermostat will work with my system.

Can you please take a look at the below images and let me know if this will be as simple as getting both cables to the same location (haven't discussed with my other half whether this new thermostat will be up, or downstairs) and hooking up control wires as the instructions state, using the wire attached to the R terminal in the thermostat set for heating for R, and cap the wire attached to the Rc terminal in the thermostat set for cooling (or vice versa)?

Below is the wiring to one of our thermostats (Set for heating):

Below is the wiring to the other thermostat (Set for cooling):

Below is where the cabling from each thermostat, and to each of the gas furnace and unit outside for electric cooling, cables converge: (The cable with the red wire wrapped around it goes to the outside box with a fan in it; the condenser? The other cables go up through inaccessible wall cavities to each thermostat, but without a continuity tester that can be used to test one wire going to different locations, assume that the cable with the blue and green wire wrapped around it at the back of this bundle is the one that goes to the heating thermostat, with the other to the cooling thermostat).

Below is the wiring block for the furnace:

The gas furnace is below a box with pipes coming from the outside cooling unit go into.

Answer 1

Your system only has 1 transformer, at the furnace

Given what we know (that the cable with the red wire back-wrapped at the junction point goes off to the outdoor unit), we can tell that the orange wire from that cable is tied into the Y connection (orange wire) from the cooling thermostat and the Y connection (yellow wire) to the furnace as well.

This means that the other (black?) wire from the cable to the outdoor unit must be connected to C for this to work in a one-transformer configuration, and indeed, it connects to the blue C wire going off to the furnace. Furthermore, the red R wire from the furnace goes out to the red wires in both thermostat cables, which is also a sign you have a one-transformer system.