How to Distribute Weight on a Table with Four Legs?

[aaron94116]

Hello,
I'm new to statics and currently working on a project where I will be placing a weight on a square rigid table at arbitrary locations, Point (x,y), and need to come up with equations to predict the weight distribution about the four legs. The weight of the table will be left out or be considered 0, so it is just the weight placed on the table that needs to be taken into account.
So far I have:

W = L1 + L2 + L3 + L4 (Weight is equal to the sum of the forces at each leg.)
L1 x1 + L2 x2 + L3 x3 + L4 x4 = 0 (moment in x-axis)
L1 y1 + L2 y2 + L3 y3 + L4 y4= 0 (moment in y-axis)

I'm considering x1, x2, y1, y2... to be the distance from the leg to the x or y point of the weight.
This is where I'm stuck and again, I'm new to statics so please correct me if my assumptions so far are incorrect.
I believe I need a fourth equation to solve for the L's but other than that I'm not quite sure where to go from here.

 

[A.T.]

I'm considering x1, x2, y1, y2... to be the distance from the leg to the x or y point of the weight.

Then express them in terms of x & y.

 

[Chestermiller]

Try doing this problem by making the sides of the table parallel to the x and y axes, and putting the center of the tabletop at the origin. Let L be the length of a side of the table. Try taking moments about the four table edges.