Solving Simultaneous Linear Equations on the TI-85 and TI-86
This is the main page for a series of pages that cover the use of the TI-85 and TI-86
to solve systems of linear equations. Below is a list of links to the pages that have been
developed, along with a description of the page. Each page has a pointer back to this
page. Each page has pointers to the appropriate previous or next page as given in
the list below. The pages are designed to be read in order, but a reader may choose
to move around as needed.
- 2 variables 2 equations simple
- A simple case for solving a system of 2 equations involving 2 variables. This page
introduces the use of the SIMULT function on the TI-85 and TI-86 calculators. It provides
a step by step detail of the keys and the screens associated with the SIMULT function.
The problem is given in standard form and the coeffients and answers are integers.
- 3 variables 3 equations simple
- Expand the problem to 3 equations with 3 unknowns. This page reinforces some of the
material presented in the previous page, and maintains simplicity by having
integer values and by having a unique solution.
- 4 variables 4 equations simple
- Expand the problem to 4 equations with 4 unknowns. This page reinforces some of the
material presented in the previous page, and maintains simplicity by having
integer values and by having a unique solution. Note that this page demonstrates
the effect of an input error and it shows correcting that error.
- 3 variables 3 equations simple with other variables.
- Return to the problem of 3 equations with 3 unknowns, but use different variables, and
start with equations that are not in standard form.
- 7 variables 7 equations simple
- Expand the problem to 7 equations with 7 unknowns. This page expands
the problem and, therefore, demonstrates having so many
variables that material scrolls off the screen.
However, this page maintains simplicity by having
integer values and by having a unique solution.
- 3 variables 3 equations simple with missing variables.
- Return to the problem of 3 equations with 3 unknowns, but use
equations that are missing some of the variables.
- 4 variables 4 equations simple with missing and other
variables.
- Return to the problem of 4 equations with 3 unknowns, but use
equations that are missing some of the variables, and uses variables other than
the standard w, x, y, z. Also, the original equations ae not given in standard form.
- 2 variables 2 equations simple, but
lines are parallel.
- Return to the problem of 2 equations with 2 unknowns, but use
equations that are parallel.
- 3 variables 3 equations simple, but two of the
planes are parallel.
- Return to the problem of 3 equations with 3 unknowns, but where two of the three
equations that are parallel, and, therefore, there is no solution.
- 3 variables 3 equations simple,
not parallel, but still no solution.
- Return to the problem of 3 equations with 3 unknowns, but where
each pair of planes intersect, but the three planes never intersect.
The lines of intersection are parallel, but are not in the
same plane. Therefore, there is no solution.
- 3 variables 3 equations simple,
with fractional coefficients and constants.
- Return to the problem of 3 equations with 3 unknowns, but we introduce
a situation where the coefficients and constants are fractions. There is a solution,
and it turns out to be integer values
- 3 variables 3 equations simple,
but with the answers being fractional values.
- Return to the problem of 3 equations with 3 unknowns, but where
the solutions turn out to be freactions. This poses a problem on the
calculator becuase the result of the "SIMULT" process is not directly
available as a ANSwer to be converted to a fraction.
- 4 variables 4 equations simple,
not parallel, but still no unique solution.
- Return to the problem of 4 equations with 4 unknowns, but where
there is no unique solution. The calculator produces the SINGULAR MATRIX error
and we return to look at the equations to discover the reason.
- 2 variables 3 equations complex,
but no unique solution.
- Look at a situation where there are 3 equations in 2 variables.
SIMULT does not allow this directly. We look at pairs of
equations to determine what is going on for all three.
- 2 variables 3 equations complex,
2 parallel, no unique solution.
- Look at a situation where there are 3 equations in 2 variables.
In this example, two of the lines are parallel and the third is a transversal,
a crossing line.
- 2 variables 3 equations complex,
a unique solution.
- Look at a situation where there are 3 equations in 2 variables.
The problem presented on this page does have all three equations intersecting in
exactly one point.
- 2 variables 3 equations complex,
2 identical and there is a unique solution.
- Look at a situation where there are 3 equations in 2 variables.
The example demonstrates having a unique solution for three equations, even in the
case where the calculator reports that there is not a unique solution for two of the
three equations.
- 3 variables 4 equations complex,
but with a unique solution.
- Look at a situation where there are 4 equations in 3 variables.
SIMULT does not allow this directly. We look at three
equations at a time. If two sets of three equaitons
have a point in common, then that point is the unique solution
for all four. This example has such a point.
- 3 variables 4 equations complex,
but without a solution.
- Look at a situation where there are 4 equations in 3 variables.
SIMULT does not allow this directly. We look at three
equations at a time. If two sets of three equaitons
have a point in common, then that point is the unique solution
for all four. In this example, there is no such point.
©Roger M. Palay
Saline, MI 48176
October, 1998