What a long innocuous title!! No, buddy! This kind of equations appear in various cases near us, especially when you face a math textbooks =)

Anyway, for you who “forget” the definitions, Simultaneous equations are two or more equations with multiple variables. A solution of those equations is a set of variables that simultaneously satisfy all equations. The linear equations are generally given as “*y = ax + b*,” while non-linear equations can be any expressions not described as linear (e.g. “5X^{3}-7Y^{2} = 21″). Does that ring a bell??Except you was sleeping during the classes, I’m sure that at least in your junior high school, you have learned about how to solve that kind of equations.

Now I wanna ask you how to solve the following equation?

x+ 2y= 1,x^{2}+y^{2}= 57

It’s easy, isn’t it? You can just take some piece of paper and pencil, then scratch like below

*x* + 2*y* = 1 ——–(1)

*x*^{2} + *y*^{2} = 57 ——–(2)

From (1): x= 1- 2*y* ——–(3)

Substitute (3) into (2): (1-2y)^{2}* +* y^{2} = 10

* *1- 4y + 4y^{2} +y^{2} = 10

5*y*^{2} – 4y -9 = 0

(5y – 9) (y +1)= 0

*y* = 9/5 or -1

Substitute the values of y into the equation (3) to find the value of x.

when y = 9/5 x = 1 -2(9/5)=-13/5

when y = -1 x = 1 -2(-1) = 3

the solution set is *x* = , *y* = 9/5

or x = 3, y =-1

By the way, the above method is called *Substitution method*.

However, the real life is not as simple as substitution method. For example, what do you think about the solution of problems below?

2. Heat (Q) balance in heat exchange instrument, simultaneous non linear equations which involve 3 unknown quantities (T_{2},t_{2}, Q):

I’m not sure you can easily solve that with only a piece of paper (but if you’re an Mathematics Olympiad Participant, a Math Professor, or just a Math Geek, perhaps I’m wrong.) And if you’re a programmer or using expensive softwares like Matlab, Mathematica, and so on, those problems are quite easy. But now, I gonna share to you how to solve it using your Microsoft Excel only. Because I have already written too much in this post, I will only solve the first problem.

First, open your Excel, then enter the equation into cell B2, just like picture below.

The step after that is the main point. If you’re using an Excel 2003, you could press [Tool]->[Goal Seek], and if you’re using an Excel 2007, you would press Data tab, then [What-If Analysys], then [Goal Seek], and the setting window would open like below.

Enter just like what excel requests us, then excel will calculate repeatedly until the value of our equation in cell B2 reach zero. See cell B1, and you have the solution for this equation, which t =359.6 Kelvin. This means that alcoholic drink would boil at 86 ℃. This method is quite simple, isn’t it??

At last, please remember keyword of the day: GOAL SEEK..

Good luck!

Problems Source:「Excelで気軽に化学工学 」 伊東 章

Thanks for all of this great information! You’ve giving us a very easy to follow tutorial. Keep up the awesome posts!

And when you get a chance head over to http://www.facebook.com/office and tell us more about your use of Excel!

Cheers,

Andy

MSFT Office Outreach

Wow, nice comment, and thanks for the information about that facebook link =)

I can’t wait for the Office 2010 to be available.

Regards

Have you tried Office 2010 Beta yet? If not here’s the download link: http://www.microsoft.com/office/2010/en/default.aspx

Thanks again for the fantastic articles! 🙂

Andy

MSFT Office Outreach Team

wow.. kerenn (yang komentar pertama maksudnya) soalnya aku ga ngerti postingannya haha..

Good Job Baharu!

Waduuuuuuuuuuuh, berarti aku gagal sebagai writer ^^

Coba dibaca pelan-pelan fa..ini cuma penyelesaian persamaan matematik biasa. Cuma aku kasih tips bagi pemakai Excel, itu aja…quite simple, isn’t it?

Aku yakin suatu saat cara ini kepake…

“…or using expensive softwares like Matlab, Mathematica, and so on, those problems are quite easy. But now, I gonna share to you how to solve it using your Microsoft Excel only…”

You don’t think MS-Office expensive? :D… I guess it isn’t that expensive for students, though :-).

Btw, great tips! I normally don’t work with those kinds of equations anymore (most engineers I know are using either conservative or simplified calculations), but you have shown us what Excel can do.

Great job! Thanks…

Thanks for the polite comment, mas Goio…

No, I don’t think excel is expensive either. In Titech, with “only” 1400 Yen, students are able to get Microsoft Office, and in ITB, it’s even cheaper: 10,000 Rupiahs for 1 year (legal) license..

Cheers :=)

Hello.

Is it possible for you to show the example with the Heat balance, involving 3 equations with 3 unknowns nonlinear?

I’ve got a similar problem and cant seem to wrap my head around it 😦

Thanks.

Christoffer.

it was a nice explanation but how to solve for three unknown of non-linear simulteneous equation just like your second example? hope you can help.

hello, is it possible to solve 2 complicated equations with two unknowns? i mean, for example, i have to compute wet bulb temperature with dry bulb temperature and vapor pressure given.. i’m really having a hard time finding out how..

thanks for any help! :))

jyn

how to solve 2 nonlinear simultaneous equations in ms-excel using goal seek or by any method in ms-excel????????? please reply….