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	<id>https://mathresearch.utsa.edu/wiki/index.php?action=history&amp;feed=atom&amp;title=Solving_Equations</id>
	<title>Solving Equations - Revision history</title>
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	<updated>2026-05-20T19:27:37Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://mathresearch.utsa.edu/wiki/index.php?title=Solving_Equations&amp;diff=4459&amp;oldid=prev</id>
		<title>Khanh at 22:50, 10 January 2022</title>
		<link rel="alternate" type="text/html" href="https://mathresearch.utsa.edu/wiki/index.php?title=Solving_Equations&amp;diff=4459&amp;oldid=prev"/>
		<updated>2022-01-10T22:50:18Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 22:50, 10 January 2022&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l26&quot; &gt;Line 26:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 26:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Division - It is said that two things are inevitable: death and taxes.  Division is the operation we use to make the inevitable fair.  When a shepherd died his heirs could use division to divide up his flock fairly. They might use a function that allocated one sheep per heir until the flock was distributed. In what ways could the heirs distribute extra sheep if the flock was not evenly divisible? Similarly, when collecting taxes it is more fair to take a portion of the flock rather than a single amount.  The clan leader would be better served taking 1/12th of a flock from each shepherd every year.  If the clan leader asked for a specific number of sheep every year they might find that their clan became smaller every year just before tax time as new shepherds took their sheep to a new clan.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Division - It is said that two things are inevitable: death and taxes.  Division is the operation we use to make the inevitable fair.  When a shepherd died his heirs could use division to divide up his flock fairly. They might use a function that allocated one sheep per heir until the flock was distributed. In what ways could the heirs distribute extra sheep if the flock was not evenly divisible? Similarly, when collecting taxes it is more fair to take a portion of the flock rather than a single amount.  The clan leader would be better served taking 1/12th of a flock from each shepherd every year.  If the clan leader asked for a specific number of sheep every year they might find that their clan became smaller every year just before tax time as new shepherds took their sheep to a new clan.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;{{TextBox|1&lt;/del&gt;= '''Thought Problem'''  &lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;blockquote style&lt;/ins&gt;=&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;quot;background: white; border: 1px solid black; padding: 1em;&amp;quot;&amp;gt;  &lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;:&lt;/ins&gt;'''Thought Problem'''  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Video Games have an attribute called &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;[[w:game play|&lt;/del&gt;game play&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;]]&lt;/del&gt;. Look at a video game you enjoy playing and try to define how you interact with the environment using addition, subtraction, multiplication, and division.   &lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;:&lt;/ins&gt;Video Games have an attribute called game play. Look at a video game you enjoy playing and try to define how you interact with the environment using addition, subtraction, multiplication, and division.   &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;/blockquote&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Using A Variable ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Using A Variable ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l87&quot; &gt;Line 87:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 88:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Manipulation of Radicals ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Manipulation of Radicals ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Let's say that we have a number &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt;.  The square root of &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the number that, if multiplied by itself, equals &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt;.   Since there are two numbers which satisfy that condition, we usually specify the positive value.  For example, the square root of 4 could be 2 (because &amp;lt;math&amp;gt;2 \times 2 = 4&amp;lt;/math&amp;gt;) or it could be -2 (because &amp;lt;math&amp;gt;-2 \times -2 = 4&amp;lt;/math&amp;gt;).  We use the symbol &amp;lt;math&amp;gt;\sqrt{x}&amp;lt;/math&amp;gt; to indicate the &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;[[Algebra/Square Root is Positive|&lt;/del&gt;positive&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;]] &lt;/del&gt;square root of &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Let's say that we have a number &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt;.  The square root of &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the number that, if multiplied by itself, equals &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt;.   Since there are two numbers which satisfy that condition, we usually specify the positive value.  For example, the square root of 4 could be 2 (because &amp;lt;math&amp;gt;2 \times 2 = 4&amp;lt;/math&amp;gt;) or it could be -2 (because &amp;lt;math&amp;gt;-2 \times -2 = 4&amp;lt;/math&amp;gt;).  We use the symbol &amp;lt;math&amp;gt;\sqrt{x}&amp;lt;/math&amp;gt; to indicate the positive square root of &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The cube root of &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the number that, if multiplied by itself three times, equals &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt;.  We use the symbol &amp;lt;math&amp;gt;\sqrt[3]{x}&amp;lt;/math&amp;gt; to indicate the cube root of &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The cube root of &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the number that, if multiplied by itself three times, equals &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt;.  We use the symbol &amp;lt;math&amp;gt;\sqrt[3]{x}&amp;lt;/math&amp;gt; to indicate the cube root of &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l196&quot; &gt;Line 196:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 197:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Basic Laws In Algebra ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Basic Laws In Algebra ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In algebra we are working with the set of real numbers.  We talked about the properties of real numbers with respect to mathematical operations in the section &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;[[Algebra/&lt;/del&gt;Real Numbers&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;|Real Numbers]]&lt;/del&gt;.  If you don't remember the Commutative Property, the Associative Property, the Distributive Property, and the Identity Property go back to the real numbers section to review them.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In algebra we are working with the set of real numbers.  We talked about the properties of real numbers with respect to mathematical operations in the section Real Numbers.  If you don't remember the Commutative Property, the Associative Property, the Distributive Property, and the Identity Property go back to the real numbers section to review them.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;There are several basic laws in algebra.  Understanding these will help you to manipulate and solve equations, and to understand algebraic relationships.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;There are several basic laws in algebra.  Understanding these will help you to manipulate and solve equations, and to understand algebraic relationships.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Khanh</name></author>
		
	</entry>
	<entry>
		<id>https://mathresearch.utsa.edu/wiki/index.php?title=Solving_Equations&amp;diff=4458&amp;oldid=prev</id>
		<title>Khanh at 22:47, 10 January 2022</title>
		<link rel="alternate" type="text/html" href="https://mathresearch.utsa.edu/wiki/index.php?title=Solving_Equations&amp;diff=4458&amp;oldid=prev"/>
		<updated>2022-01-10T22:47:11Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;a href=&quot;https://mathresearch.utsa.edu/wiki/index.php?title=Solving_Equations&amp;amp;diff=4458&amp;amp;oldid=935&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>Khanh</name></author>
		
	</entry>
	<entry>
		<id>https://mathresearch.utsa.edu/wiki/index.php?title=Solving_Equations&amp;diff=935&amp;oldid=prev</id>
		<title>Lila: Created page with &quot;* [https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Elementary_Algebra_(OpenStax)/05%3A_Systems_of_Linear_Equations/5.01%3A_Solve_Systems_of_Equations_by_Graphing Solvi...&quot;</title>
		<link rel="alternate" type="text/html" href="https://mathresearch.utsa.edu/wiki/index.php?title=Solving_Equations&amp;diff=935&amp;oldid=prev"/>
		<updated>2021-09-11T23:57:21Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;* [https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Elementary_Algebra_(OpenStax)/05%3A_Systems_of_Linear_Equations/5.01%3A_Solve_Systems_of_Equations_by_Graphing Solvi...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;* [https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Elementary_Algebra_(OpenStax)/05%3A_Systems_of_Linear_Equations/5.01%3A_Solve_Systems_of_Equations_by_Graphing Solving Systems of Equations by Graphing], Mathematics LibreTexts&lt;br /&gt;
* [https://math.libretexts.org/Courses/Monroe_Community_College/MTH_098_Elementary_Algebra/5%3A_Systems_of_Linear_Equations/5.2%3A_Solve_Systems_of_Equations_by_Substitution Solving Systems of Equations with Substitution], Mathematics LibreTexts&lt;br /&gt;
* [https://math.libretexts.org/Courses/Monroe_Community_College/MTH_098_Elementary_Algebra/5%3A_Systems_of_Linear_Equations/5.3%3A_Solve_Systems_of_Equations_by_Elimination Solving Systems of Equations with Elimination], Mathematics LibreTexts&lt;/div&gt;</summary>
		<author><name>Lila</name></author>
		
	</entry>
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