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  <question type="stack">
    <name>
      <text>3.4.1.5 Solve simultaneous</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>

<p>Solve the following equations to find the values of \(x\) and \(y\)</p>

<ol class="HELM_parts">
    <li>
        <p>\[{@sysl1[1,1]@}={@sysr1[1,1]@}\]</p>
        <p>\[{@sysl1[2,1]@}={@sysr1[2,1]@}\]</p>
        <div>\({@B1@}=\) [[input:ans1]] [[validation:ans1]] [[feedback:prt1]]</div>
    </li>

    <li>
        <p>Solve the following equations to find the values of \(x\) and \(y\)</p>
        <p>\[{@sysl2[1,1]@}={@sysr2[1,1]@}\]</p>
        <p>\[{@sysl2[2,1]@}={@sysr2[2,1]@}\]</p>
        <div>\({@B2@}=\) [[input:ans2]] [[validation:ans2]] [[feedback:prt2]]</div>
    </li>

    <li>
        <p>Solve the following equations to find the values of \(x\) and \(y\)</p>
        <p>\[{@sysl3[1,1]@}={@sysr3[1,1]@}\]</p>
        <p>\[{@sysl3[2,1]@}={@sysr3[2,1]@}\]</p>
        <div>\({@B3@}=\) [[input:ans3]] [[validation:ans3]] [[feedback:prt3]]</div>
    </li>
</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<ol class="HELM_parts">
    <li>
        <p>\[{@sysl1[1,1]@}={@sysr1[1,1]@}\]</p>
        <p>\[{@sysl1[2,1]@}={@sysr1[2,1]@}\]</p>
        <p>We modify the equations so that x can be eliminated. For example by multiplying the first equation by {@A1[2,1]@} and the second by {@A1[1,1]@} we find:</p>
        <p>\[{@expand(A1[2,1]*sysl1[1,1])@}={@A1[2,1]*sysr1[1,1]@}\]</p>
        <p>\[{@expand(A1[1,1]*sysl1[2,1])@}={@A1[1,1]*sysr1[2,1]@}\]</p>
      <p>If these equations are now added we can eliminate \(x.\) Therefore</p>
        <p>\({@B1@}= {@ta1@}\)</p>
    </li>

    <li>
        <p>Solve the following equations to find the values of \(x\) and \(y\)</p>
        <p>\[{@sysl2[1,1]@}={@sysr2[1,1]@}\]</p>
        <p>\[{@sysl2[2,1]@}={@sysr2[2,1]@}\]</p>
        <div>\({@B2@}= {@ta2@}\)</div>
    </li>

    <li>
        <p>Solve the following equations to find the values of \(x\) and \(y\)</p>
        <p>\[{@sysl3[1,1]@}={@sysr3[1,1]@}\]</p>
        <p>\[{@sysl3[2,1]@}={@sysr3[2,1]@}\]</p>
        <div>\({@B3@}= {@ta3@}\)</div>
    </li>
</ol>]]></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(matrix([1,2],[3,4]))+matrix([2,-5],[2,2]);
B1:matrix([x],[y]);
sysl1:A1.B1;
ta1:rand(matrix([3],[3]))+matrix([-6],[1]);
sysr1:A1.ta1;

A2:rand(matrix([1,3],[5,1]))+matrix([3,2],[5,-3]);
B2:matrix([x],[y]);
sysl2:A2.B2;
ta2:rand(matrix([1],[3]))+matrix([-3],[1]);
sysr2:A2.ta2;

A3:rand(matrix([1,2],[3,4]))+matrix([2,2],[2,2]);
B3:matrix([x],[y]);
sysl3:A1.B1;
ta3:rand(matrix([1],[3]))+matrix([-25],[2]);
sysr3:A3.ta3;</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\[{@sysl1=sysr1@}, \quad {@B1=ta1@}\]
\[{@sysl2=sysr2@}, \quad {@B2=ta2@}\]
\[{@sysl3=sysr3@}, \quad {@B3=ta3@}\]</text>
    </questionnote>
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      <text/>
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      <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>
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    <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>
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    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
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