You should clear of fractions first.

Clear the first of fractions by multiplying 
through by : 



   2x - 9y = -30

Clear the second of fractions by multiplying 
through by : 



   9x + 4y = 132

So we have the system

   2x - 9y = -30
   9x + 4y = 132

The coefficients of y are -9 and 4. The LCD of
their absolute values is 36, so 

1. We need to make the -9 in the first into a -36 
by multiplyng the whole first equation through by 4.
2. We need to make the 4 in the second into a 36 
by multiplyng the whole second equation through by 9.

(4)2x - (4)9y = (4)(-30)
(9)9x + (9)4y = (9)(132)

which simplified becomes:

     8x - 36y = -120
    81x + 36y = 1188

Add term by term vertically

     8x - 36y = -120
    81x + 36y = 1188
   ------------------
    89x       = 1068

Divide through by 89

            x = 1068/89
            x = 12

Sunstitute 12 for x in

    2x - 9y = -30

 2(12) - 9y = -30
    24 - 9y = -30
        -9y = -30 - 24
        -9y = -54
          y = (-54)/(-9)
          y = 6

So the solution is (x,y) = (12,6).

Edwin