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Your equations are then:

B1 - C1 = 46

B2 - C2 = 8

B1 + B2 = 663

C1 + C2 = 609

B3 - C3 = 54

D1 + D2 = 54

Now enter known cells to Excel sheet:

D1 = 46

D2 = 8

B3 = 663

C3 = 609 (not necessary for calculations because it is dependent on other values)

D3 = D1 + D2 (not necessary for calculations because it is dependent on other values)

Then you may simply iterate the result by following formulas entered into Excel sheet:

B1 = B3 - B2

B2 = D2 + C2

C1 = B1 - D1

C2 = B2 - D2

To allow iterations in Excel go to the Tools - Options - Calculations and set number of iterations to e.g. 100 and Excel will calculate the result for you:

B1 = 1118 (Yours X)

B2 = -455 (Mine X)

C1 = 1072 (Yours Y)

C2 = -463 (Mine Y)

Iteration.xls