The number of girls, g, in a room is four more than two times the number of boys, b. Half of the number of girls in the room minus the number of boys is 2. The equations below represent the situation. g=4+2b1/2 g-b=2

It is evident that you need to find the solution of the system, if it exists.

Let's work the equations.

The second equation (which corresponds correctly to the second statement) is:

g/2 - b = 2, which you can be transformed in this way:

1) Multiply by 2 => g - 2b = 4

2)  Transpose - 2b => g = 4 + 2b.

Now you can see that this equation is the same than the firs equation, which means that the second statement does not provide any new information.

Mathematically, this is a system with infinite solutions, and you cannot determine the number of boys or girls without more information which provides and independent equation.

Answer: there are infinite solutions to the system.