Simple 3 equation 3 variable, with fractional coefficients, integer answers

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 situation, no solution, non-parallel.
The next example page covers a Simple 3 equation 3 variable situation, with integer coefficients, but fractional 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

and the

key will be shown as

, again to save space.

The problem we will use on this page is (2/3)x - (4/5)y - (1/2)z = -133/30
(5/3)x - (9/2)y + (8/5)z = -257/6
(6/7)x - (5/8)y + (4/3)z = -2143/168

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 first coefficient is 2/3, which we enter via . Then to move to the second coefficient we press the key. When we do that, the 2/3 on the screen is converted to .66666666666667. We enter the second coefficient, -4/5, via the keys. Then to move to the third coefficient we press the key. When we do that, the -4/5 on the screen is converted to -.8. We enter the third coefficient, -1/2, via the keys. Having entered the third coefficient, we press the key to move to the constant term. When we do that, the -1/2 on the screen is converted to -.5. Finally, we enter the constant, -133/30, via the keys. This is the state shown in 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, namely, 5/3, 9/2, 8/5, and -257/6. The key sequence enters those values and completes Figure 3.

Figure 4 We leave Figure 3 by pressing the key. The calculator shifts to the screen in Figure 4, asking for the coefficients and constant value for the third equation, namely, 6/7, -5/8, 4/3, and -2143/168. The key sequence enters those values and completes Figure 4.

Figure 5 Figure 5 demonstrates the effect of pressing the key after Figure 4. The -2143/168 is converted to the decimal value -12.75595280952, with the cursor sitting on top of the negative sign. With our without the "enter" key, at the end of Figure 4 or here on Figure 5, we are ready to obtain the answers.

Figure 6 Pressing the key causes the calculator to produce the answers, shown in Figure 6. In this case, even with the fractional coefficients, the answers come out as integer values, namely, x=-2, y=7, and z=-5.

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 first coefficient is 2/3, which we enter via . Then to move to the second coefficient we press the key. When we do that, the 2/3 on the screen is converted to .66666666666667. We enter the second coefficient, -4/5, via the keys. Then to move to the third coefficient we press the key. When we do that, the -4/5 on the screen is converted to -.8. We enter the third coefficient, -1/2, via the keys. Having entered the third coefficient, we press the key to move to the constant term. When we do that, the -1/2 on the screen is converted to -.5. Finally, we enter the constant, -133/30, via the keys. This is the state shown in 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, namely, 5/3, 9/2, 8/5, and -257/6. The key sequence enters those values and completes Figure 3.
Figure 4	We leave Figure 3 by pressing the key. The calculator shifts to the screen in Figure 4, asking for the coefficients and constant value for the third equation, namely, 6/7, -5/8, 4/3, and -2143/168. The key sequence enters those values and completes Figure 4.
Figure 5	Figure 5 demonstrates the effect of pressing the key after Figure 4. The -2143/168 is converted to the decimal value -12.75595280952, with the cursor sitting on top of the negative sign. With our without the "enter" key, at the end of Figure 4 or here on Figure 5, we are ready to obtain the answers.
Figure 6	Pressing the key causes the calculator to produce the answers, shown in Figure 6. In this case, even with the fractional coefficients, the answers come out as integer values, namely, x=-2, y=7, and z=-5.