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2.1 - Linear Equations and Modeling

2.1 - Linear Equations and Modeling -

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<?xml version="1.0" encoding="utf-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>2.1 - Linear Equations and Modeling</title> <link href=". ./m116.css" rel="stylesheet" type="text/css" /> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> </head> <body> <h1>2.1 - Linear Equations and Modeling</h1> <h2>Definitions</h2> <dl> <dt>Equation</dt> <dd>A statement that two expressions are equal</dd> <dt>Solutions</dt> <dd>Values which make the equation true</dd> <dt>Identity</dt> <dd>An equation which is true for every real number in the domain</dd> <dt>Contradiction</dt> <dd>An equation which is false for every real number in the domain</dd> <dt>Conditional equation</dt> <dd>An equation which may be true or false depending on the values of the variables.</dd> <dt>Equivalent equations</dt> <dd>Equations having the same solution set.</dd> <dt>Linear equation in one variable</dt> <dd>Equation that can be written as ax+b=0, where a and b are reals and a doesn't equal zero. If a did equal zero, it would be a constant equation and an identity if b=0 or a contradiction if b≠0.</dd> <dt>Extraneous solutions</dt> <dd>Solutions which satisfy an &quot;equivalent&quot; equation, but not the original equation. They can be introduced by multiplying or dividing by an expression containing a variable. They can also be introduced by applying a non-one-to-one function to both sides (like squaring both sides). You should always check your answer when there is a possibility that you have introduced an extraneous solution.</dd>
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This note was uploaded on 10/18/2011 for the course MAT 1033 taught by Professor Brown during the Spring '10 term at Valencia.

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2.1 - Linear Equations and Modeling -

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