2x - 3y =  18,     (1)
5x + 9y = -10.     (2)

Multiply equation (1) by 5 (both sides) and equation (2) by 2. You will get

10x - 15y =  90,   (3)
10x + 18y = -20.   (4)

Now distract equation (3) from equation (4) (both sides). You will get

-15y - 18y = 90 -(-20),

-33y = 110,

y =  =  = -.

Then from (1)  x =  =  =  = 4.

Answer. x = 4, y = -.