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      <text>3.4.1.3 Introduction no solution</text>
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      <text><![CDATA[<h3><span>Equations with no solution</span><br></h3>

<p>On occasions we may encounter a pair of simultaneous equations which have no solution. Consider the following example.</p> 

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<h4 class="HELM_example">Example</h4>
<p>Show that the following pair of simultaneous equations have no solution.</p>
<p>\(10x - 2y = -3\) &nbsp; (9)</p> 
<p>\(-5x + y = 1\) &nbsp; (10)</p>
<h4 class="HELM_solution">Solution</h4>
<p>Leaving equation (9) unaltered and multiplying equation (10) by 2 we find</p>

<p>\(10x - 2y = -3\)</p>
<p>\(-10x + 2y = 2\)</p>

<p>Adding these equations to eliminate \(x\) we find that \(y\) is eliminated as well:</p>

<p>\(10x - 2y = -3\)</p>
<p>\(-10x + 2y = 2\) &nbsp; Add</p>
<p>\(0x + 0y = -1\)</p>

<p>The last line '\(0=-1\)' is clearly nonsense.</p>

<p>We say that Equations (9) and (10) are <strong>inconsistent</strong> and they have <strong>no solution</strong>.</p>]]></text>
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