Solving systems of equations of TI-89

averagemathgeek
Tue, 17 May 2005 17:57:42 +0000

“One more question–how can I tell which variable will have an infinite number of solution, so that I know how to express the other ones in terms of that variable?”

In your example, the solution to the system looks like this:

x=-1/7-t/7
y=5/7+5t/7
z=t
Where t can be any real number

As you can tell, each variable can take on an infinite number of values. Thus, rather than saying an individual variable has infinite solutions, you should say the system has infinite solutions. You may think this is petty. However, consider another set of solutions to the same system:

x=s
y=-5s
z=-1-7s
where s can be any real number

You find that these two sets of solutions are identical.

Hope this clears up the general understanding of the solution. It is a topic (including the link between the two solutions) covered in great depth in linear algebra.