### Simple 4 equation 4 variable

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.
The next example page covers a Simple 3 equation 3 variable situation, with other variables.

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.

2x + 5y - 9z + 3w = 151
5x + 6y - 4z + 2w = 103
3x - 4y + 2z + 7w = 16
11x + 7y + 4z - 8w = -32

We are looking for the values of the variables that make all four equations true. [Remember that these are linear equations in four variables. In the earlier example of two variables in two equations, we could associate the problem with lines on in a Cartesian plane where each equation represents a line. In the 3 equation 3 variable situation we could associate each equation with a plane in Cartesian space. For 4 equations and 4 variables we no longer have the luxury of a physical model. Nonetheless the observations of the earlier situations hold true. There are an infinite number of 4 values (one for each of x, y, z, and w) that make each equation true. In the problem given above, there is exactly one set of 4 values that make all four equations true. We need to find that set of 4 values, for x, y, z, and w, that solve all four equations.]

Before we actually start using the calculator, remember that the calculator will be using a general form for each of the equations, expecting the equations to have the variables is the same order. The earlier pages had much longer explanations of this. Here we will just point out that the calculator will use
 ai,j for the coefficient of the jth variable in the ith equation. Thus, a2,3 is the coefficient for the 3rd variable in the 2nd equation. xj for the jth variable. Thus, x4 is the fourth variable (in our case w). bi is the constant value in the ith equation. Thus b3 is the constant value in the third equation.

Now, onto the problem on the calculator.

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.
The next example page covers a Simple 3 equation 3 variable situation, with other variables.