Excel's Formula - sisman

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424 Part V: Miscellaneous <strong>Formula</strong> Techniques 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 y. The following represents the first equation, 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 X, and cell B6 is named Y. The formulas in these cells 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.
Figure 16-7: This worksheet solves two simultaneous equations. Chapter 16: Intentional Circular References 425 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.
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Excel ® Microsoft 2010 ® Microsof
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Excel® 2010 Formulas Published by
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Publisher’s Acknowledgments We’
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vi Part VII: Appendixes Appendix A:
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viii Keyboard shortcuts . . . . . .
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x Potential Problems with Names . .
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xii Date-Related Functions . . . .
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xiv Working with Tables . . . . . .
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xvi Chapter 13: Financial Schedules
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xviii Creating Links to Cells . . .
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xx Excel’s Auditing Tools . . . .
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xxii Does the text match a pattern?
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1 INTRODUCTION Welcome to Excel 201
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770 Index array formulas (continued
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5. Limited Warranty. (a) WPI warran
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