1. 3x + 4y=25

2. 2x -  5y=9

We could rewrite these as follows by multiplying the first equation by 5 and the second by 4:

1. 15x + 20y=125

2. 8x    -  20y=  36

If we add the above two equations, we can eliminate y:

23x         = 161

So x = 7, and plugging this into the first equation we can figure out y:  21 + 4y = 25, so y = 1