4x - 5y = -18
 3x + 2y =  -2

To eliminate y, we observe the coefficients of y.
They are -5 and +2.  If we ignore signs the least
common multiple of 5 and 2 is 10, so we multiply 
the first equation through by 2 to make y have a 
coefficient of -10 and the second equation by 5 to
make y have a coefficient of -10:

 8x - 10y = -36
15x + 10y = -10

Then we add them vertically term by term:

 8x - 10y = -36
15x + 10y = -10
———————————————
23x       = -46
        x = -2

Substitute -2 for x in

   3x + 2y = -2
3(-2) + 2y = -2
   -6 + 2y = -2
        2y = 4
         y = 2

The solution is (x,y) = (-2,2)

Edwin