Did older Airliners use a pitot-static system?
They used the same kind of pitot probes and static ports as modern aircraft, but prior to the 70s they didn't use Air Data Computers  that processed the pitot static information in a central location for electronic distribution to other systems that needed the data (that had to wait for the Integrated Circuit and Microprocessor revolutions of the 60s).

Prior to that the pitot and static pressure was routed directly to the instruments and devices that needed to measure it, so you had the plumbing itself routed to both the pitot static instruments and electronic devices that needed it, pretty much like with light aircraft, but with way more plumbing.  The adoption of ADCs reduced the plumbing requirements to just that required between the probes and ports and the ADCs.

Computations and conversions of pressure data (like deriving Mach#) were done by analog mechanical or electronic means directly within the instruments themselves. 

So, an airplane like a 707 in the late 50s would have lots and lots of low pressure pneumatic plumbing running up behind the instrument panels and to various analog computing devices in the avionics bay.