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      <text>3.4.1.4 Introduction infinite solutions</text>
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      <text><![CDATA[<h3><span>Equations with an infinite number of solutions</span><br></h3>

<p>Some pairs of simultaneous equations can possess an innite number of solutions. Consider the
following example.</p> 

<hr>
<h4 class="HELM_example">Example</h4>
<p>Solve the equations.</p>
<p>\(2x + y = 8\) &nbsp; (11)</p> 
<p>\(4x + 2y = 16\) &nbsp; (12)</p>
<h4 class="HELM_solution">Solution</h4>
<p>If  Equation (11) is multiplied by 2  we find both equations are identical:</p>
<p>\(4x + 2y   = 16\).</p>
<p>This means that one of them is redundant and we need only consider the single equation&lt;\p&gt; 
</p><p>\(2x + y = 8\)</p>

<p>There are infinitely many pairs of values of \(x\) and \(y\) which satisfy this equation. For example, if \(x=0\) then \(y=8\), if \(x=1\) then \(y=6\), and if \(x=-3\) then \(y=14\). We could continue like this producing more and more solutions. Suppose we choose a value, say \(\lambda\), for \(x\). We can then write</p>

<p>\(2\lambda + y = 8\) so that \(y= 8-2\lambda\)</p>

<p>The solution is therefore \(x=\lambda\), \(y=8-2\lambda\) <strong>for
any value of \(\lambda\) whatsoever</strong>. There are an <strong>infinite</strong> number
of such solutions.</p>]]></text>
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