Simple 3 equation 3 variable, but with no solution, non-parallel.

The main page for solving systems of linear equations on the TI-85 and TI-86.
The previous example page covers a Simple 3 equation 3 variable, but two parallel planes.
The next example page covers a Simple 3 equation 3 variable situation, with fractional coefficients, but integer answers.

WARNING: The TI-85 and TI-86 are almost identical in their use of the SIMULT function. The major difference is the labels that are on certain keys. On the TI-85, SIMULT is the 2nd function on the

key, whereas on the TI-86 SIMULT is the 2nd function on the

key. When a difference is important it will be presented in the text below. The exception to this is the "3" key. On the TI-85 it appears as

, while on the TI-86 it is

. To save some space, and to ignore this difference, the numeric keys (the gray ones) have been changed here to only show the key face, as in

. In addition, the

key will be shown as

, again to save space.

The problem we will use on this page is 22x + 32y - 7z = 234
9x - 5y - 30z = -49
13x + 37y + 23z = 482

Figure 1 The keystrokes to start this process are the same on the two calculators, although the keys have a different name. For the TI-85 we start with and , but for the TI-86 we start with and . On either calculator this selects the "SIMULT" function. The calculator responds with a request for the value of "Number" as shown in Figure 1. The SIMULT function expects to have exactly the same number of equations as we have variables. For our problem, we have 3 variables and 4 equations. Therefore we respond with the key to complete Figure 1.
Figure 2 We leave Figure 1 by pressing the key. The calculator shifts to the screen in Figure 2, asking for the coefficients and constant value for the first equation. The key sequence enters those values and completes Figure 2.

Figure 3 We leave Figure 2 by pressing the key. The calculator shifts to the screen in Figure 3, asking for the coefficients and constant value for the second equation. The key sequence enters those values and completes Figure 3.
Now we can move to the next screen by pressing the key.

Figure 4 In Figure 4 we need to enter the coefficients and constants for the third equation, in our standard form, namely 13, 37, 23, and 482. We use the keys to complete the image of Figure 4.
We have entered all of the values. We are ready to solve the system of linear equations.

At this point, on eithter the TI-85 or the TI-86, we are ready to press the key to request a solution. Unfortunately, the two calculators produce differenet results. As shown in Figure 5 below, the TI-86 produces the error message that indicates that there are no solutions. Unfortuneately, the TI-85 produces a solution, although it is an impossible one. This is shown in Figure 6 below.

Figure 5 - For TI-86 Only

We request a solution by pressing the key. The TI-86 calculator displays the error message in Figure 5.
We could press to quit the SIMULT processing, or we could press to return to the data entry phase of the SIMULT processing, giving us a display that is essentially the same as was given in Figure 2. We would do this so that we could display and change if need be the coefficients and constant terms. In this case, the values were entered correctly. We could simply quit the processing. (Skip Figure 6.)

Figure 6 - For TI-85 Only
We request a solution by pressing the key. The TI-85 calculator displays the values shown in Figure 6. This indicates a solution at x=1.24375E14, y=-7.4625E13, and z=4.975E13. These are huge numbers. The E means "times 10 to the power of". For example, x=1.24375E14 could written out as 124,375,000,000,000. Given that the coefficients of the equations are relatively small integer values, there is little likelihood that the calculator's answre is correct. We can use our calculator to check the answer, and we will see that such values are wrong. These values do not make any of the original equations work. Thus, even though the TI-85 produces an answer, we need to be somewhat suspicious, especially if the answer invovles huge values.

Figure 1	The keystrokes to start this process are the same on the two calculators, although the keys have a different name. For the TI-85 we start with and , but for the TI-86 we start with and . On either calculator this selects the "SIMULT" function. The calculator responds with a request for the value of "Number" as shown in Figure 1. The SIMULT function expects to have exactly the same number of equations as we have variables. For our problem, we have 3 variables and 4 equations. Therefore we respond with the key to complete Figure 1.
Figure 2	We leave Figure 1 by pressing the key. The calculator shifts to the screen in Figure 2, asking for the coefficients and constant value for the first equation. The key sequence enters those values and completes Figure 2.
Figure 3	We leave Figure 2 by pressing the key. The calculator shifts to the screen in Figure 3, asking for the coefficients and constant value for the second equation. The key sequence enters those values and completes Figure 3. Now we can move to the next screen by pressing the key.
Figure 4	In Figure 4 we need to enter the coefficients and constants for the third equation, in our standard form, namely 13, 37, 23, and 482. We use the keys to complete the image of Figure 4. We have entered all of the values. We are ready to solve the system of linear equations.