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Suppose there are P people and F flies.

Then 13 heads implies: P + F = 13

and 46 legs implies: 2*P + 6*F = 46

Sibtracting twice the first equation from the second gives:

4*F = 20 so that F = 5

and then P = 13 - F = 8

So 8 people and 5 flies.

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