"Niek Otten" wrote in message
...
<This can be completely solved analytically

I know, Harlan. Many complex problems can be solved analytically. We don't
need computers at all, apart from solving crossword
puzzles.

But I'm sure I'm not alone in preferring an iterative approach if there is
an easy one.
If the first equation would have been more complex, I wouldn't even have
tried.

Ten lines of algebra is ten lines of possible errors. It is for me. I'm
sure it is for some others. I'm certain it is for the many
who are not familiar with the algebraic approach.

I think your limit of 10 lines is just *your* figure. Nothing to do with
an objective limit.

I will not try to turn this forum into a math class.
I admit there are posters who are better helped with some education, like
in the many questions about percentages.

--
Kind regards,

Niek Otten
Microsoft MVP - Excel




"Harlan Grove" wrote in message
...
| "Niek Otten" wrote...
| Can probably done using Solver. I'm more used to Goal seek, so I
| rework to one variable
|
| I use cell A2 for x and B2 for y.
|
| Reworking 21x+6y=10:
| x = (10-6y)/21
| So the formula in A2 is:
| =(10-6*B2)/21
| ...
|
| Not enough algebra. This can be completely solved analytically. Just
| substitute your expression for x based on the first equation into the
| second equation. First simplify: 6y appears in both equations, so
| replace it with z = 6y.
|
| 21x + z = 10
| (7x - 20)^2 + (z + 10)^2 = 200
|
| z = 10 - 21x
|
| Then substitute the RHS for z in the second equation.
|
| (7x - 20)^2 + (10 - 21x + 10)^2 = 200
| (7x - 20)^2 + (20 - 21x)^2 = 200
| 49x^2 - 280x + 400 + 400 - 840x + 441x^2 = 200
| 490x^2 - 1120x + 800 = 200
| 49x^2 - 112x + 60 = 0
|
| So x has 2 solutions
|
| 56/49 + (3136/2401 - 60/49)^0.5 and 56/49 - (3136/2401 - 60/49)^0.5
|
| and y also has two solutions. Solver will only find one, depending on
| the initial state of the variable cell. Also, the Solver solution is
| approximate while the analytical solution is accurate to machine
| precision. Finally, as any who uses numerical analysis in their job
| will tell you, if all it takes is 10 or fewer lines of algebra to
| reach an exact solution, that ALWAYS preferable to ANY iterative
| approach.

++++++++++++++++++++++++++++++++++++++++++++++++=
Using Solver to solve these equation sets is a disaster. You cannot rely on
the accuracy of the results, which generally are only accurate to 2-3
decimal digits. Most of the time it is not accurate to any decimal digit.
The algorithm is faulty.

David Heiser