Simple 2 equation 2 variable, parallel lines

The main page for solving systems of linear equations on the TI-85 and TI-86.
The previous example page covers a Simple 4 equation 4 variable situation but with missing and other varaibles.
The next example page covers a Simple 3 equation 3 variable situation, but with no solution since two planes are parallel.

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 3x + 4y = 14
3x + 4y = 21

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 2 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 first equation. The key sequence enters those values and completes Figure 3. We are ready to request the solution.

For TI-85 only: Figure 4

Note that Figure 4 is only for the TI-85. Skip to Figure 5 for the TI-86.
We request a solution by pressing the key. The TI-85 responds with Figure 4. Here it does seem that there is an answer. A value is given for both x₁ and x₂. However, these values are so far from being reasonable that we need to use them as an indication that there is a problem. The first answer is -9.33333333333E13. This is the scientific form for a number that we would write as -93,333,333,333,300. the second value, 7E13 we would write as 70,000,000,000,000. It is possible to have two lines cross at that point, but not the two lines for this problem.
Skip to the paragraph below Figure 5.

For TI-86 only: Figure 5

Note that Figure 5 is only for the TI-86. Go back to Figure 4 for the TI-85.
We request a solution by pressing the key. The TI-86 responds with Figure 5. This is an error message. It indicates that we can not solve these simultaneous equations because they produce a "SINGULAR MATRIX". This means that the TI-86 can not determine a unique solution for the coefficients and constants that have been given.
Our choices are on the menu at the bottom of the screen. We can "QUIT" or "GOTO". The "QUIT" option will take us out of the process of solving simultaneous equations. It returns the TI-86 to its normal calculator mode. The "GOTO" option will return the TI-86 to the first "coefficient" screen, as shown in Figure 2. This will allow us to check and possibly change the coefficients and constants.

If we return to the original problem,

3x + 4y = 14
3x + 4y = 21 we can see that the two lines are parallel. The lines that represent these equations will never cross. They have the same slope, but different intercepts. There can not be a point such that 3 times the x-value plus 4 times the y value gives 14 one time and 21 the next.

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 2 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 first equation. The key sequence enters those values and completes Figure 3. We are ready to request the solution.
For TI-85 only: Figure 4	Note that Figure 4 is only for the TI-85. Skip to Figure 5 for the TI-86. We request a solution by pressing the key. The TI-85 responds with Figure 4. Here it does seem that there is an answer. A value is given for both x₁ and x₂. However, these values are so far from being reasonable that we need to use them as an indication that there is a problem. The first answer is -9.33333333333E13. This is the scientific form for a number that we would write as -93,333,333,333,300. the second value, 7E13 we would write as 70,000,000,000,000. It is possible to have two lines cross at that point, but not the two lines for this problem. Skip to the paragraph below Figure 5.
For TI-86 only: Figure 5	Note that Figure 5 is only for the TI-86. Go back to Figure 4 for the TI-85. We request a solution by pressing the key. The TI-86 responds with Figure 5. This is an error message. It indicates that we can not solve these simultaneous equations because they produce a "SINGULAR MATRIX". This means that the TI-86 can not determine a unique solution for the coefficients and constants that have been given. Our choices are on the menu at the bottom of the screen. We can "QUIT" or "GOTO". The "QUIT" option will take us out of the process of solving simultaneous equations. It returns the TI-86 to its normal calculator mode. The "GOTO" option will return the TI-86 to the first "coefficient" screen, as shown in Figure 2. This will allow us to check and possibly change the coefficients and constants.