Answer:
There are 25 geese and 16 goats
Step-by-step explanation:
Let O represent the # of goats and E the # of geese.  Remembering that goats have four feet and geese only two, and that each animal has only one head, we can write the following equations to determine O and E:
Number of heads:  41; this is the total of the # of goat heads and the # of goose heads:  O + E = 41
(4 feet per goat)O + (2 feet per goose)E = 114 (There are a total of 114 feet)
Then we solve the following system of linear equations:
   O   +   E   =    41
  4O   +   2E  = 114
Multiplying the first equation by -2 results in -2O  - 2E  = -82.
Combining this result with the second equation, we obtain the system
  4O  +  2E  =  114
  -2O  - 2E  = -82
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   2O =   32
Then O = # of goats = 32/2, or 16, and so the equation O   +   E   =    41 becomes 
          E  = # of geese =  41 - O (remembering that we found O to be 16), or
          E  =  41 - 16  = 25
There are 25 geese and 16 goats.