How Is Tension Calculated in an Atwood Machine?

[RufusTFirefly]

With an Atwood Machine, I understand that the formula for calculating T can be calculated with two simultaneous equations.

T-m1g=m1a

a= (m2 - m1
(

T – m1

 

[Astronuc]

Compare those equations with -

http://hyperphysics.phy-astr.gsu.edu/hbase/atwd.html#c1