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### Types of Linear Systems

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Date: 10/13/97 at 16:30:20
From: John
Subject: Types of linear systems

In my math class Al/Geo/Sat 2, I was told to find out what is meant
when a type of linear system is said to be a consistent or an
inconsistent system.

I have looked up this question in a few math books and have asked 3
or 4 teachers without any success. Can you help?

Thanks a lot,
John
```

```
Date: 10/13/97 at 17:32:42
From: Doctor Scott
Subject: Re: Types of linear systems

Hi John!

Since you are talking about linear systems, it might be helpful to
think about the possibilities when you graph the equations that make
up the system.

If the system consists of 2 equations, there are 3 possibilities
when you graph the equations:

(1) The lines may cross at ONE point. This point is usually called
the solution of the system.

(2) The lines may be coincident (lie on on another). There are
infinitely many solutions to the system. In fact, any point that
lies on the line is a solution.

(3) The lines may be parallel. There are NO solutions to the system.

When the system leads to (3), it is usually called INCONSISTENT.
There is no solution that is common to the two equations.  Note that
we can tell if a system is inconsistent without actually graphing it
by looking at the slopes of the lines and their y-intercepts. If the
slopes are the same but the y-intercepts are different, the lines are
parallel and not the same line.

When (2) occurs, the system is said to be DEPENDENT.

I would guess that (1) would be called CONSISTENT.

-Doctor Scott,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Equations, Graphs, Translations
High School Linear Algebra

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