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    <name>
      <text>3.4.1.6 Write and solve simultaneous</text>
    </name>
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      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>A straight line has equation of the form \(y = ax + b\). The line passes through the points with coordinates \(({@c1@}, {@c2@})\) and \(({@c3@}, {@c4@})\). Write down the simultaneous equations which must be satisfied by \(a\) and \(b\).</p>

<p>\( {@c2@} = \) [[input:ans1]] [[validation:ans1]]</p>
<p>\( {@c4@}= \) [[input:ans2]] [[validation:ans2]]</p>

<p>Solve the equations and hence find the equation of the line.<br></p>
<p>\(y = \) [[input:ans3]] [[validation:ans3]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>A straight line has equation of the form \(y = ax + b\) and passes through the points with coordinates \(({@c1@}, {@c2@})\) and \(({@c3@}, {@c4@})\).</p>
<p>The simultaneous equations which must be satisfied by \(a\) and \(b\) are:</p>
<p>\[{@c2@}={@ta1@}\]</p>
<p>
</p>
<p>\[{@c4@}={@ta2@}\]</p>
<p>
</p>
<p> We solve the equations and find \( a = {@aa@}\) and \(b= {@bb@}.\)</p>
<p>Hence, the equation of the line is: \[ y= {@ta3@}\]</p>]]></text>
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    <stackversion>
      <text>2021072200</text>
    </stackversion>
    <questionvariables>
      <text>c1: rand(5) + 5; 
c2: 4; 
c3: rand(3) + 1; 
c4: 3;

aa: (c2-c4)/(c1-c3);
bb: c4 - c3*((c2-c4)/(c1-c3));

ta1: a*c1+b;
ta2: a*c3+b;
ta3: ((c2-c4)/(c1-c3))*x + c4 - c3*((c2-c4)/(c1-c3));</text>
    </questionvariables>
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      <text><![CDATA[<p>[[feedback:prt1]]</p><p>[[feedback:prt2]]</p><p>[[feedback:prt3]]<br></p>]]></text>
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    <questionnote format="moodle_auto_format">
      <text>\({@c2@}={@ta1@}, \quad {@c4@}={@ta2@}, \quad y={@ta3@}\)</text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
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