To find the values of p and q, we can use the given solution of x = 1 and y = 2.
Substituting these values into the first equation, we get:
3x - py = 4
3 * 1 - p * 2 = 4
3 - 2p = 4
-2p = 1
p = -1/2
Substituting these values into the second equation, we get:
4x - 3y + q = 0
4 * 1 - 3 * 2 + q = 0
4 - 6 + q = 0
-2 + q = 0
q = 2
So the solution to the system of equations is x = 1, y = 2, p = -1/2, and q = 2.