#### Answer

Number of goats = 14
Number of chickens = 9

#### Work Step by Step

Let the number of goats be x and number of chickens be y.
Thus we can say total number of animals will be,
$x+y=23$
Each goat has 4 legs and chicken has 2, thus we get
$4x+2y=74$
Now get have two equations and two variables.
On multiplying the first by 2 and subtracting it from second we get,
$(4x+2y)-2(x+y)=74-2\times23$
$4x+2y-2x-2y=28$
$2x=28$
Therefore,
$x=14$
On putting it back in equation 1 we get,
$y=9$
Number of goats = 14
Number of chickens = 9