Align your system of linear equations so that the same variables occupy the same space so that all constants are on the right side of the equation. If a variable does not exist for one of the linear equations, make its coefficient zero. For example, consider the following system of linear equations:
3x + 5z -- y = 10
x -- y + 1 = -1
2y -- 3z + x = 1
becomes ...
3x -- y + 5z = 10
x -- y + 0z = -2
x + 2y -- 3z = 1
Note: If a term does not change its side of the equation, its sign does not change.
Create the matrices that you will store into your calculator.
[A] = the coefficients (multipliers) of the variables in order.
| 3 -1 5 |
| 1 -1 0 |
| 1 2 -3 |
[B] = the solutions to the equations in order of their correspondence to the coefficients.
| 10 |
| -2 |
| 1 |
Store the matrices into your calculator. On most graphing calculators, you will hit the "2nd" key and then "MATRX" to access the matrix program. Scroll to "EDIT," choose matrix [A]. Hit "ENTER." Matrices are built as rows x columns. In this case, put in 3 x 3. Then fill in the information corresponding to the numbers of matrix [A] from Step 2. Once finished, quit the MTRX program and then restart the MTRX program, this time building matrix [B], which will be a 3 x 1 matrix.
Once your matrices are built, go to the MTRX program and choose matrix [A] under "NAMES." It will show up as [A] on your home screen. Hit the "X^-1" key, or inverse key, which should appear under the "MATH" program key. Then go back to the "MTRX" program and choose [B] under "NAMES." Hit "ENTER" and then hit "ENTER" again on the home screen to calculate the answers.
Interpret your results. Based on the order you put our variables, the solutions will be in the form of x = first entry, y = second entry and z = third entry. In this case, the solution on the home screen should read as follows:
| 1 |
| 3 |
| 2 |
Where x = 1, y = 3 and z = 2 are the solutions to our linear equations.