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rbeezer committed 56f51f5

Minor edits, Section SSLE

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src/section-SSLE.xml

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 <introduction>
-<p>We will motivate our study of linear algebra by considering the problem of solving several linear equations simultaneously.  The word <q>solve</q> tends to get abused somewhat, as in <q>solve this problem.</q>  When talking about equations we understand a more precise meaning:  find <em>all</em> of the values of some variable quantities that make an equation, or several equations, true.</p>
+<p>We will motivate our study of linear algebra by considering the problem of solving several linear equations simultaneously.  The word <q>solve</q> tends to get abused somewhat, as in <q>solve this problem.</q>  When talking about equations we understand a more precise meaning:  find <em>all</em> of the values of some variable quantities that make an equation, or several equations, simultaneously true.</p>
 
 </introduction>
 
 <subsection acro="SLE">
 <title>Systems of Linear Equations</title>
 
+<p>Our first example is of a type we will not purse further.  While it has two equations, the first is not linear.  So this is a good example to come back to later, especially after you have seen <acroref type="theorem" acro="PSSLS" />.</p>
+
 <example acro="STNE" index="solving nonlinear equations">
 <title>Solving two (nonlinear) equations</title>
 
 
 <p>We are about to give a rather involved proof, so a discussion about just what a theorem really is would be timely.  Stop and read <acroref type="technique" acro="T" /> first.</p>
 
-<p>In the theorem we are about to prove, the conclusion is that two systems are equivalent.  By <acroref type="definition" acro="ESYS" /> this translates to requiring that solution sets be equal for the two systems.  So we are being asked to show <em>that two sets are equal</em>.  How do we do this?  Well, there is a very standard technique, and we will use it repeatedly through the course.  If you have not done so already, head to <acroref type="section" acro="SET" /> and familiarize yourself with sets, their operations, and especially the notion of set equality, <acroref type="definition" acro="SE" /> and the nearby discussion about its use.</p>
+<p>In the theorem we are about to prove, the conclusion is that two systems are equivalent.  By <acroref type="definition" acro="ESYS" /> this translates to requiring that solution sets be equal for the two systems.  So we are being asked to show <em>that two sets are equal</em>.  How do we do this?  Well, there is a very standard technique, and we will use it repeatedly through the course.  If you have not done so already, head to <acroref type="section" acro="SET" /> and familiarize yourself with sets, their operations, and especially the notion of set equality, <acroref type="definition" acro="SE" />, and the nearby discussion about its use.</p>
+
+<p>The following theorem has a rather long proof.  This chapter contains a few very necessary theorems like this, with proofs that you can safely skip on a first reading.  You might come back to them later, when you are more comfortable with reading and studying proofs.</p> 
 
 <theorem acro="EOPSS" index="equation operations">
 <title>Equation Operations Preserve Solution Sets</title>
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