Excel Algebra help

[Paykempton]

Hello all, I need to create an excel spreadsheet that can solve a system of linear equations by only entering the a, b, c, d, e, and f of:

ax + by = c
dx + ey = f

I am a rookie at excel and algebra. So when explaining on how to do this please treat me as such. I need to know exactly what formulas to enter in what locations.

I appreciate any and all help I can get.
Thank you

 

[mikerickson]

If you put a in A1, b in B1, C in D1 , d in A2, e in B2 and f in D2,

Then select two rows and one column and enter the array formula
=MMULT(MINVERSE(A1:B4),D1:D2) with Ctrl-Shift-Enter (Cmd+Return for Mac) the values for x and y will be returned

<table border=1 cellspacing=0>
<tr align="center" bgcolor=#A0A0A0><td width=25> <td width=25><b>A</b><td width=25><b>B</b><td width=25><b>C</b><td width=25><b>D</b><td width=25><b>E</b><td width=25><b>F</b></tr>
<tr><td align="center" bgcolor=#A0A0A0><b>1</b><td align="right" bgcolor=#FFFFFF>1<td align="right" bgcolor=#FFFFFF>2<td align="left" bgcolor=#FFFFFF><td align="right" bgcolor=#FFFFFF>5<td align="left" bgcolor=#FFFFFF><td align="right" bgcolor=#FFFFFF>1</tr>
<tr><td align="center" bgcolor=#A0A0A0><b>2</b><td align="right" bgcolor=#FFFFFF>3<td align="right" bgcolor=#FFFFFF>4<td align="left" bgcolor=#FFFFFF><td align="right" bgcolor=#FFFFFF>11<td align="left" bgcolor=#FFFFFF><td align="right" bgcolor=#FFFFFF>2</tr>
</table>

 

[mirabeau]

Hello all, I need to create an excel spreadsheet that can solve a system of linear equations by only entering the a, b, c, d, e, and f of:

ax + by = c
dx + ey = f

I am a rookie at excel and algebra. So when explaining on how to do this please treat me as such. I need to know exactly what formulas to enter in what locations.

I appreciate any and all help I can get.
Thank you

Supposing a in A1, b in B1, C in D1 , d in A2, e in B2 and f in D2.

Then in F1 enter =(B2*D1-B1*D2)/(A1*B2-A2*B1)
and in F2 enter =(A1*D2-A2*D1)/(A1*B2-A2*B1)

These are given just in case you don't follow or aren't familiar with the matrix operations MINVERSE and MMULT.

The formulae above follow directly from the very basic successive (or Gauss-Jordan) elimination of variables in simultaneous, linear, consistent and linearly independent equations. They actually involve fewer actual arithmetic operations than the matrix inversion/multiplication approach, although this latter approach is likely to be much more convenient if using Excel.

 

[mikerickson]

Paykempton, Discussion is more fruitful in thread than in PM's.

"Are there formulas I have to enter in A1 and such so that it knows what to do with that cell?"

No, A1 is a precedent cell.

Excel formulas do not put data they get data.

In this case the formula in F1:F2 gets the data from A1:B2 and D1:D2 to make determine its result. This relationship is reflected in the terminology that F1:F2 are called Dependent Cells and A1:B2,D1:D2 are called Precedent cells.

To get the result that you want, enter the numbers in the precedent cells.
Then select F1:F2, type =MMULT(MINVERSE(A1:B4),D1:D2) and press Ctrl-Shift-Enter simultaneously.

You are done. To find the solution to a different problem, you do not need to re-enter the formula in F1:F2, just change the data in A1:B2,D1:D2.

 

[Paykempton]

Thanks so much for the help. I have it figured out now. You are awesome! !