The opposite sides of a rectangle are equal, so we can write the following equations:
2x = 3y + 5 ...........(1)
x = 2y + 2 .............(2)
Multiply equation (2) by 2, to get:
2x = 4y + 4 ...........(3)
The right hand sides of equations (1) and (3) are equal, so we can write:
3y + 5 = 4y + 4
which gives y = 1 as the solution.
Plugging y = 1 into equation (2), we find the x = 4.
So the full solution is: x = 4, y = 1.