We need to make one of the terms in one the equations equivalent to one of the terms in the other equation.

The easiest way to do this would be to multiply everything in the first equation by 3:

9p + 6q = 27

4p - 6q = 25

Adding these equations together cancels the 'q' terms, so we are left with 13p = 52 which gives p = 4.

Substitute p = 4 into one of the equations: (3x4) + 2q = 9

12 + 2q = 9

2q = -3

q = -1.5

Check with the other: (4x4) - (6x-1.5) = 25

As that equation is meant to equal 25, that means that I got it right.