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<quiz>
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    <name>
      <text>PT.7.11 (One lin. one quad. sim. eqns no factorise 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 lists e.g. if you believe the solutions are (x=1,y=2) and (x=3, y=4) enter <code>[[x=1,y=2],[x=3,y=4]]</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 \(y\) on its own. We can then set the two equations equal to each other and rearrange to obtain a quadratic in \(x\) in standard form. In this case we have 
\[
{@eqn1b@} = {@eqn2b@} 
\]
Solving this quadratic gives us the values of \(x\).Then substituting the values into one of the initial equations we obtain the answer. In this case {@ta1@}.</p>]]></text>
    </generalfeedback>
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    <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(10);

eqn1: a1*x^2 +a2*x + a3 = y;
eqn2: b1*x +b2 = y;

eqn1b: a1*x^2 +a2*x + a3;
eqn2b: b1*x +b2;

ta1: solve([eqn1,eqn2],[x,y]);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>{@eqn1@}, {@eqn2@}, {@ta1@}</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>
    </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>
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    <complexno>i</complexno>
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</quiz>
