Microsoft Office Tutorials and References
In Depth Information
Circular Reference Examples
Figure 16-6: This workbook uses circular references to calculate several recursive equations.
Solving simultaneous equations using a circular reference
In some cases, you can use circular references to solve simultaneous equations. Consider the two
simultaneous equations listed here:
3x + 4y = 8
3x + 8y = 20
You need to find the value of x and the value of y that satisfies both equations. First, rewrite the
equations to express them in terms of x and The following represents the first equation, y.
expressed in terms of x:
x = (8 – 4y)/3
The following equation represents the second equation, expressed in terms of y:
y = (20 – 3x)/8
As shown in Figure 16-7, cell B5 is named and cell B6 is named The formulas in these cells Y.
mirror the previous equations. The formula in B5 (X) is
=(8–(4*Y))/3
The formula is cell B6 (Y) is
=(20–(3*X))/8
The figure also shows a chart that plots the two equations. The intersection of the two lines
represents the values of X and Y that solve the equations.

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