Microsoft Office Tutorials and References

In Depth Information

**Circular Reference Examples**

Figure 16-7:
This worksheet solves two simultaneous equations.

Note the circular reference. The X cell refers to the Y cell, and the Y cell refers to the X cell. These

cells converge to display the solution:

X = –1.333

Y = 3.000

Using intentional circular references to solve simultaneous equations is more of an interesting

demonstration than a practical approach. You’ll find that some iterative calculations never

converge. In other words, successive recalculations will never hone in on a solution. For example,

consider the simultaneous equations that follow. A solution does indeed exist, but you cannot use

circular references to find it.

x = 4 – y/2

y = 3 + 2x

Using matrices is a better approach for solving simultaneous equations with Excel. See

Chapter 10 for examples.

The companion CD-ROM contains the workbook
simultaneous equations.xlsx

with two sets of simultaneous equations. You can solve one set by using intentional

circular references; you cannot solve the other set using this technique.