I'll chime in here with a little more technical info. Hope you can follow. The above is correct though!
First of all, all jet aircraft that are pressurized use bleed air tapped off of the engines at different stages before combustion. You have low pressure and high pressure. Usually when the aircraft is at idle or low power settings, air is taken from the high pressure stage. As the engine RPM increases, it switches to low pressure. On Learjets we use "Modulating Valves" on older ones, 60's use a "Mixing Valve), and the 45 uses a bunch of different valves to mix air. Here is a little test you can do next time you ride on a commercial aircraft. When you board the aircraft and sit down, turn on the overhead air full blast. When sitting at the gate, the plane usually has the Auxillary/Airborn Power Unit (APU) running. This is essentially a small jet engine that has a generator, hyd pumps, etc hooked to it. It is designed to run at 100% RPM regardless of load. More load more fuel. This is usually the last thing the engineers cram into the aircraft tail or wheel well. They always make it a real ***** to work around. This APU also supplies air to the cabin for that air conditioning your feeling at the gate. This APU also supplies air to the starters on the main engines. When you start the "pushback" and the pilot starts the engines, notice what the air does. It usually stops, as all or most of the air is diverted to the air starter on the engine. Also you'll notice the lights flicker as they bring on the engine generator and split the load between the engine and APU. One other thing that is interesting. The more air you take from the engine, or bleed, the hotter it runs and less power it has. If it is really hot, most likely they shut off the A/C for a few minutes to get the power they need. Also, the same goes for when the weather is bad. If conditions are right and they have to take-off with wing anti-ice on, kiss the a/c good by! When I am trouble shooting problems on engines, I often use the ITT (interstage turbine temp) guage to read what the engine is doing. You can tell so much from this guage. If I have a split between engines, I know one has a leak. Air is leaking from the engine, so usually that means it runs hotter. That is of course if the engines have similar total time on them. We have had several #3 carbon seals go out lately, and you guessed it. The cabin fills up with burning oil smokey stuff. It really scares the passengers and sometimes makes the pilots seat cushions dissappear. Hope this helps. Any other questions and I'd be glad to help!
Nik