I. Function Keys
K. SIMULT
You can solve up to 30 linear equations with 30 unknowns using the Simultaneous Equation Solver.
Example: Solve the system of equations using SIMULT.
Press
.


Enter a 3 since
there are 3 equations and 3 unknowns. 

Enter the
coefficients and the constant for each equation. 

Press ENTER
and the next set of numbers. 

Third equation.


Press
(SOLVE).

The solution to this system is x=8/3, y=11, z=26/3.
The disadvantage to this function is that you cannot have the calculator put the answers in fraction form, so you will not be able to get exact values. However, it is a very useful function for checking work, and to test a system to see if there is a solution.
What happens if the system has no solution or infinite solutions? You will get the error message shown in the example below. There is no distinction made between no solution and infinite solutions. To determine the correct outcome, you can either use algebra techniques of row reduction or you can use the matrix capabilities of your TI86.
Example: Enter the information for the system below to see the result your calculator shows for a system of equations with no solution. (The result shown is the same if the system has infinite solutions.)
Press
and enter 3. 

Enter equation 1.


Enter equation2.


Enter equation 3.


Result when
(SOLVE) is pressed. 
The message that the result is a singular matrix only indicates that there is either no solution or infinite solutions.