How to Use Excel to Solve System of Linear Equations

The system of equations (simultaneous equations) is two or more equations with multiple variables. Simultaneous linear equations can written in the general form as a1X + b1Y = c1 and a2X + b2Y = c2. A solution of such a system is a set of variables "X" and "Y" that simultaneously satisfy these equations. The letters "a1," "a2," "b1," "b2," "c1" and c2 abbreviate the numeric coefficients in equations. One method of solving such linear equations is to use Cramer's rules, which involves calculations of determinants for three matrixes that are comprised from the equation coefficients. This method is easy to implement in Microsoft Excel using the program's formulas feature. As an example, solve the following linear equations: 4X - 5Y=14 and 3X-8Y= -16.

Instructions

Creating an Excel File

1. Open Microsoft Excel and press "Ctrl-N" to create a new document.

2. Click on the cell "A3" and press the key "=" on the keyboard. Type the following string "A1*B2-A2*B1" and press "Enter."

3. Click on the cell "B3" and press the key "=" on the keyboard. Type the following string "C1*B2-C2*B1" and press "Enter."

4. Click on the cell "C3" and press the key "=" on the keyboard. Type the following string "A1*C2-A2*C1" and press "Enter."

5. Click on the cell "A5" and press the key "=" on the keyboard. Type the following string "B3/A3" and press "Enter."

6. Click on the cell "C5" and press the key "=" on the keyboard. Type the following string "C3/A3" and press "Enter."

7. Select the cells "A5" through "C5" by holding the left mouse button. Then release the mouse button. Right-click on the select cells and choose "Format Cells." Select the tab "Number."

8. Select "Number" under "Category." Type "3" in the field "decimal places" and click "OK." Note that equation solution values will be displayed as rounded to thousandth. This precision is sufficient in the most cases.

9. Press "Ctrl-S." Type a descriptive file name, for example, "Solve Equations" and press "Save" for saving the file on your computer.

Solving the System of Equations

1. Open Microsoft Excel and press "Ctrl-O." Browse your computer and open the file created in Section 1.

2. Enter the coefficients of the first equation ("a1" "b1" and "c1") in the cells "A1," "B1," and "C1" of the file. For our example, type "4" "-5" and "14" in those cells.

3. Enter the coefficients of the second equation ("a2" "b2" and "c2") in the cells "A2," "B2," and "C2" of the file. For this example, type "3" "-8" and "-16" in those cells.

4. Read the equation solution that becomes available instantly. The values of the variables "X" and "Y" will be displayed in the cell "A5" and "C5" respectively. In this example, "X" = 11.294 and "Y"= 6.235.

Tips & Warnings

• Section 1 is a one time procedure. Once the Excel file is created, go directly to Steps in Section 2.

References

• Using Cramer's Rule
• "Excel 2007: The Missing Manual", Matthew MacDonald, Pogue Press, Dec. 27, 2006.