2x - 9y = -5
4x - 6y = 2
multiple first equation by 2:
4x - 18y = -10
4x - 6y = 2
Subtract 2 from 1:
-12y = -12
y = 1
Now plug y=1 into any equation. I go with second:
4x - 6(1) = 2
4x - 6 = 2
4x = 8
x = 2
So the solution is (2,1) therefore there is one solution.