If all were pheasants, there would be 35 pairs of feet. There are 47 pairs of feet, so there must be 47-35 = 12 rabbits. Each rabbit has one more pair of feet than a pheasant does.
There are 12 rabbits and 23 pheasants.
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If you insist on equations, you can let p and r represent the numbers of pheasants and rabbits, then write ...
... p + r = 35
... 2p + 4r = 94
Divide the second equation by 2 and subtract the first:
... (2p +4r)/2 - (p +r) = (94)/2 - (35)
... r = 12 . . . . . . . . . . . simplify
... p + 12 = 35 . . . . . . use the value of r in the first equation
... p = 23 . . . . . . . . . . subtract 12
(p, r) = (23, 12)
