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  <question type="stack">
    <name>
      <text>3.4.1.10 Use a graph to solve simultaneous</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>

<p>Use graphs to solve the following pairs of simultaneous equations.<br></p>

<p>\[{@sysl1[1,1]@}={@sysr1[1,1]@}, \quad (eq1)\]</p>
<p>\[{@sysl1[2,1]@}={@sysr1[2,1]@}, \quad (eq2)\]</p>
<p>By rearranging into the standrd form for tte equation of a straight line we get:</p>
<p>\( eq1: \quad y= \)&nbsp;[[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</p>
<p>\( eq2: \quad y = \)&nbsp;[[input:ans2]] [[validation:ans2]] [[feedback:prt2]]<br></p>
<p>By drawing the graphs we find that the two lines intersect at the point:</p>
<div>\({@B1@}=\) [[input:ans3]] [[validation:ans3]] [[feedback:prt3]]</div>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>We are given the equations:</p>
<p>\[{@sysl1[1,1]@}={@sysr1[1,1]@}, \quad (eq1)\]</p>
<p>\[{@sysl1[2,1]@}={@sysr1[2,1]@}, \quad (eq2)\]</p>

<p>By rearranging into the standrd form for tte equation of a straight line we get:</p>
<p>\( eq1: \quad y= {@eq1@}\)</p>
<p>\( eq2: \quad y = {@eq2@}\)</p>

<p>Now we draw the graphs of the two lines:</p>
<p>{@plot([eq1, eq2], [x,s1-3,s1+3], grid2d, [yx_ratio, 1],[legend, true] )@}</p>
<p>We find that the two lines intersect at the point:</p>
<div>\({@B1@}= {@ta@}\)</div>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2021120900</text>
    </stackversion>
    <questionvariables>
      <text>ordergreat(x,y);

a1: rand([2,4]);
b1: rand([3,5])
A1: matrix([a1,-a1],[b1,1]);
B1:matrix([x],[y]);
sysl1:A1.B1;
s1: -(rand(4)+2);
s2: rand_with_prohib(-4,-1,[s1]);
ta:matrix([s1],[s2]);
sysr1:A1.ta;

eq1: (a1*x)/a1-sysr1[1,1]/a1;
eq2: -b1*x+sysr1[2,1];</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\[{@sysl1=sysr1@}, {@B1=ta@}\]</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
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    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
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      <name>ans1</name>
      <type>algebraic</type>
      <tans>eq1</tans>
      <boxsize>10</boxsize>
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      <type>matrix</type>
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