#### Answer

There are 14 goats and 9 chickens.

#### Work Step by Step

1) g + c = 23
2) 4g + 2c = 74
---------------------------------------------
First of all we make c the subject of both equation 1) and 2) .
"g + c = 23" can be rearranged into "c = 23 - g". This is done by changing +g into -g on the other side of the equal sign.
"4g + 2c = 74" can be rearranged into "c = 37 - 2g". The following steps show how this is rearranged:
1) 4g + 2c = 74
2) 2c = 74 - 4g
3) c = 37 - 2g
We can now solve this simultaneously by making both the equations equal to each other:
c = 23 - g
c = 37 - 2g
23 - g = 37 - 2g
23 = 37 - 2g + g
23 = 37 - g
23 - 37 = -g
-14 = -g
g = 14
So there are 14 goats.
To find the value of c, we can substitute g = 14 into the equation, "g + c = 23":
g + c = 23
14 + c =23
c = 23-14
c = 9
So there are 9 chickens.