Write the system so that the terms of like variables
line up vertically like this

4a + 9b       = 8
8a      + 6c = -1
     6b + 6c = -1

The letter c does not appear in the first equation, thus 
c is already eliminated from the first equation

So we will eliminate c from the other two equations.

We multiply the 3rd equation by -1 and add it to the
2nd equation 

8a      + 6c = -1
    -6b - 6c =  1
-----------------
8a - 6b      =  0

That can be divided through by 2

4a - 3b = 0

Now we have a system of 2 equations in 2 unknowns a and b

4a + 9b = 8
4a - 3b = 0

Multiplying the bottom equation by -1 and adding to the first
equation:

 4a + 9b = 8
-4a + 3b = 0
------------
     12b = 8
       b = 
       b = 

Substituting that into

4a - 3b = 0
4a - 3 = 0
4a - 2 = 0
    4a = 2
     a = 
     a = 

Substituting b =  into the original
3rd equation:

6b + 6c = -1
6· + 6c = -1
 4 + 6c = -1
     6c = -5
      c = 

Solution (a, b, c) = (,,)  

Edwin