If in a triangle Ab=2x+3, Ac=3y+1, Bd=x, Dc=y+1 find the values of x and y?

You have unknowns A, B, D, b, c, d, x, and y -- seven unknowns and only four equations. The number of equations must be equal to the number of unknowns. I suspect that you are merely in the habit of hitting the Shift key at odd moments. In any case you need to explain the problem more fully.