Types of Linear SystemsDate: 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/ |
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