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# Knowledge Base

## Solution 13062: Solving a System of Equations on the TI-89 Family, TI-92 Plus, and Voyage™ 200 Using the Gauss-Jordan method.

### How can I solve a system of equations on the TI-89 Family, TI-92 Plus, and Voyage 200 using the Gauss-Jordan method?

The TI-89 family, TI-92 Plus, and Voyage 200 graphing calculators do not have a one-key Gauss-Jordan method function. However, if you know what transformations you want to accomplish on a matrix, there are several commands available that allow the user to add or swap rows as it is done when using the Gauss-Jordan method.

Example: Solve the following system of equations:

3X + 5Y = 10
-2X + 4Y = 5

Solution:

The matrix for this example (consisting of the coefficients of the terms in the equations) is given below:

bb = [ [3 5 10] [-2 4 5 ]]

1. Enter the matrix bb into the Data/Matrix Editor Please note that on the TI-92 Plus and Voyage 200 please disregard pressing [ALPHA]:

• If the Apps Desktop is turned off press [APPS] [6] [3]. If turned on press [APPS] to display the Apps Desktop, then select Data/Matrix Editor App and press [ENTER] [3].
• Press [►] [2] [▼] [▼].
• Press [B] [B] [▼].
• Press [ALPHA] [2] [▼].
• Press [3].

• Press [ENTER] [ENTER].
• Press [3] [ENTER] [5] [ENTER] [1] [0] [ENTER].
• Press [-] [2] [ENTER] [4] [ENTER] [5] [ENTER].

2. Perform the row operations to put the matrix in reduced row echelon form:

• Press [HOME].
• Press [2ND] [MATH] [4] [ALPHA] [J] [2].
* Note: You can quickly access the command by pressing [CATALOG] and scrolling down to find it.

• Press [ALPHA] [B] [ALPHA] [B] [,] [2] [,] [1] [)].
• Press [STO►] [ALPHA] [B] [ALPHA] [B].
• Press [ENTER].

• Press [2ND] [MATH] [4] [ALPHA] [J] [4].
• Press [2] [,] [ALPHA] [B] [ALPHA] [B] [,] [1] [,] [2] [)].
• Press [STO►] [ALPHA] [B] [B].
• Press [ENTER].

• Press [2ND] [MATH] [4] [ALPHA] [J] [3].
• Press [1] [/] [2] [2] [,] [ALPHA] [B] [ALPHA] [B] [,] [2] [)].
• Press [STO►] [ALPHA] [B] [ALPHA] [B].
• Press [ENTER].

• Press [2ND] [MATH] [4] [ALPHA] [J] [4].
• Press [-] [9] [,] [ALPHA] [B] [ALPHA] [B] [,] [2] [,] [1] [)].
• Press [STO►] [ALPHA] [B] [ALPHA] [B].
• Press [ENTER].

The matrix is now in reduced row echelon form and the last column is the solution. The solutions are 15/22 for X and 35/22 for Y.

For additional information on using matrix operations and other functions on the TI-89 family, TI-92 Plus, and Voyage 200 refer to the online guidebooks.