To solve this system of equations, we can set them equal to each other and then solve for one variable:

3x + 4y = 61
4y + 3x = 72

From the second equation, we can solve for y:
4y = 72 - 3x
y = (72 - 3x) / 4

Now we can substitute this expression for y into the first equation:
3x + 4((72 - 3x) / 4) = 61
3x + 72 - 3x = 61
72 = 61
This is a contradiction, so there is no solution to this system of equations.