Geometry ​

The diagonals of a parallelogram bisect each other

So this implies that 

DH  =  HF        and   GH  = HE

So

x + 3  =  3y      rearrange as    x  -  3y  =  - 3     (1)

4x - 5  = 2y + 3 rearrange as    4x - 2y  = 8  ⇒   2x  - y  =  4   (2)

Multiply (1)  by  -2  and we have that

-2x + 6y = 6          add this to  (2)  and we get that

5y  = 10   divide both sides by 2

y  = 2 

And using (1)

x - 3(2) =  - 3

x - 6  =  -3      add 6 to both sides

x =  3

So   {x, y}   =   {3, 2)