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<quiz>
  <question type="stack">
    <name>
      <text>PT.7.7 (Two linear sim. eqns with fractions 2)</text>
    </name>
    <questiontext format="moodle_auto_format">
      <text><![CDATA[<p>Solve the simultaneous equations:
\[
\begin{align*}
{@eqn1@}
\\
{@eqn2@}
\end{align*}
\]
</p>
<p>Give your answer as a list of equations e.g. <code>[x=2,y=3]</code></p>
<p>[[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="moodle_auto_format">
      <text><![CDATA[<p>To solve these simultaneous equations we rearrange one of the equations to get either \(x\) or \(y\) on their own. Substituting this into the other equation gives us one variable. Then substituting the values into one of the initial equations we obtain the answer. in this case {@ta1@}.</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2020081700</text>
    </stackversion>
    <questionvariables>
      <text>a1: 1+ rand(5);
a2: 1+ rand(5);
a3: 1+ rand(5);
b1: 1+ rand(5);
b2: 1+ rand(5);
b3: 1+ rand(5);

eqn1: a1*x + a2*y=a3
eqn2: -b1*x + b2*y=b3




ta1: solve([eqn1,eqn2],[x,y])[1];</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>{@eqn1@}, {@eqn2@}, {@ta1@}</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <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>none</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
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    <variantsselectionseed/>
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      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta1</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint>[x=?,y=?]</syntaxhint>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
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      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>1</checkanswertype>
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      <showvalidation>1</showvalidation>
      <options/>
    </input>
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      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
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        <text/>
      </feedbackvariables>
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        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>setify(ans1)</sans>
        <tans>setify(ta1)</tans>
        <testoptions/>
        <quiet>0</quiet>
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        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>prt1-1-F</falseanswernote>
        <falsefeedback format="html">
          <text/>
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    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta1</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
