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Algorithm used by "Reduce" function


Hello,

Does anyone happen to know the algorithm used by the "Reduce" function? 
For instance:

In[1]:=      Reduce[{10x + 5y + z == 10, x + y + z == 1, x â?¥ 0, y â?¥ 0, 
z â?¥ 0}, {x, y, z}]

Out[1]=     x == 1 && y == 0 && z == -y

How does it achieve this answer?

Thanks,
Jim


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