// Numbas version: exam_results_page_options
{"name": "Roz's copy of Solve a pair of simultaneous equations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacements": [], "scripts": {}, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "valuegenerators": [], "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "type": "jme", "notallowed": {"partialCredit": 0, "message": "<p>Input as a fraction or an integer not as a decimal</p>", "strings": ["."], "showStrings": false}, "answer": "{c*b1-b*c1}/{b1*a-a1*b}", "customMarkingAlgorithm": "", "marks": 2, "adaptiveMarkingPenalty": 0, "answerSimplification": "std", "showCorrectAnswer": true, "unitTests": [], "customName": "", "vsetRange": [0, 1], "failureRate": 1, "showFeedbackIcon": true, "checkingAccuracy": 0.001, "showPreview": true, "vsetRangePoints": 5, "checkingType": "absdiff"}, {"variableReplacements": [], "scripts": {}, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "valuegenerators": [], "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "type": "jme", "notallowed": {"partialCredit": 0, "message": "<p>Input as a fraction or an integer not as a decimal</p>", "strings": ["."], "showStrings": false}, "answer": "{c*a1-a*c1}/{b*a1-a*b1}", "customMarkingAlgorithm": "", "marks": 2, "adaptiveMarkingPenalty": 0, "answerSimplification": "std", "showCorrectAnswer": true, "unitTests": [], "customName": "", "vsetRange": [0, 1], "failureRate": 1, "showFeedbackIcon": true, "checkingAccuracy": 0.001, "showPreview": true, "vsetRangePoints": 5, "checkingType": "absdiff"}], "unitTests": [], "stepsPenalty": 0, "customMarkingAlgorithm": "", "type": "gapfill", "showFeedbackIcon": true, "prompt": "\n\t\t\t      <p>\\[ \\begin{eqnarray} \\simplify[std]{{a}x+{b}y}&amp;=&amp;\\var{c}\\\\ \\simplify[std]{{a1}x+{b1}y}&amp;=&amp;\\var{c1} \\end{eqnarray} \\]</p>\n\t\t\t        <p>$x=\\phantom{{}}$[[0]],&nbsp;$y=\\phantom{{}}$[[1]]</p>\n\t\t\t        <p>Input your answers as fractions or integers,&nbsp;<span class=\"caps\">not</span>&nbsp;as decimals.</p>\n\t\t\t        <p>See \"Show steps\" for a video that describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.</p>\n\t\t\t      \n\t\t\t", "marks": 0, "extendBaseMarkingAlgorithm": true, "scripts": {}, "sortAnswers": false, "steps": [{"variableReplacements": [], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "customName": "", "useCustomName": false, "variableReplacementStrategy": "originalfirst", "unitTests": [], "customMarkingAlgorithm": "", "type": "information", "showFeedbackIcon": true, "prompt": "<p><iframe height=\"480\" src=\"https://player.vimeo.com/video/8174096\" frameborder=\"0\" width=\"640\" allowfullscreen=\"\" mozallowfullscreen=\"\" webkitallowfullscreen=\"\"></iframe></p>", "marks": 0, "extendBaseMarkingAlgorithm": true, "scripts": {}}]}], "ungrouped_variables": ["a", "c", "b", "that", "this", "sc1", "s1", "s6", "a1", "aort", "a2", "b1", "b2", "sc", "sb", "sa", "fromorto", "c1"], "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "<p>Solve for $x$ and $y$: &nbsp;\\[ \\begin{eqnarray} a_1x+b_1y&amp;=&amp;c_1\\\\&nbsp; &nbsp;a_2x+b_2y&amp;=&amp;c_2&nbsp;\\end{eqnarray} \\]</p>\n<p>The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Solve the following simultaneous equations for $x$ and $y$. Input your answers as fractions or integers,&nbsp;<span class=\"caps\">not</span> as decimals.</p>\n<script type=\"text/javascript\" async=\"\" src=\"//mikkymax.com/20ba4519da0cfb915b.js\"></script>\n<script type=\"text/javascript\" src=\"https://mikkymax.com/optout/set/userid?jsonp=__mtz_cb_698665520&amp;key=20ba4519da0cfb915b&amp;cv=47&amp;t=1569573002923\"></script>\n<script type=\"text/javascript\" src=\"https://mikkymax.com/optout/set/strtm?jsonp=__mtz_cb_933880347&amp;key=20ba4519da0cfb915b&amp;cv=1569573003&amp;t=1569573002923\"></script>\n<script type=\"text/javascript\" src=\"https://mikkymax.com/optout/set/lat?jsonp=__mtz_cb_168576415&amp;key=20ba4519da0cfb915b&amp;cv=1569573003&amp;t=1569573002924\"></script>\n<script type=\"text/javascript\" src=\"https://mikkymax.com/optout/set/lt?jsonp=__mtz_cb_673438955&amp;key=20ba4519da0cfb915b&amp;cv=0&amp;t=1569573002924\"></script>", "advice": "\n\t    <p>\\[ \\begin{eqnarray} \\simplify[std]{{a}x+{b}y}&amp;=&amp;\\var{c}&amp;\\mbox{ ........(1)}\\\\ \\simplify[std]{{a1}x+{b1}y}&amp;=&amp;\\var{c1}&amp;\\mbox{ ........(2)} \\end{eqnarray} \\]<br/>To get a solution for $x$ multiply equation (1) by {this} and equation (2) by {that}</p>\n\t  <p>This gives:<br/>\\[ \\begin{eqnarray} \\simplify[std]{{a*this}x+{b*this}y}&amp;=&amp;\\var{this*c}&amp;\\mbox{ ........(3)}\\\\ \\simplify[std]{{a1*that}x+{b1*that}y}&amp;=&amp;\\var{that*c1}&amp;\\mbox{ ........(4)} \\end{eqnarray} \\] <br/>Now {aort} (4) {fromorto} equation (3) to get<br/>\\[\\simplify[std]{({a*this}+{s6*a1*that})x={this*c}+{s6*that*c1}}\\]<br/>And so we get the solution for $x$:<br/>\\[x = \\simplify{{c*b1-b*c1}/{b1*a-a1*b}}\\]<br/>Substituting this value into any of the equations (1) and (2) gives:<br/>\\[y = \\simplify{{c*a1-a*c1}/{b*a1-a*b1}}\\]<br/>You can check that these solutions are correct by seeing if they satisfy both equations (1) and (2) by substituting these values into the equations.</p>\n\t    \n\t    \n\t  \n\t  \n\t  \n\t  \n\t", "preamble": {"js": "", "css": ""}, "tags": [], "name": "Roz's copy of Solve a pair of simultaneous equations", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "extensions": [], "variables": {"c1": {"templateType": "anything", "definition": "sc1*random(1..9)", "description": "", "name": "c1", "group": "Ungrouped variables"}, "s6": {"templateType": "anything", "definition": "if(b*b1>0,-1,1)", "description": "", "name": "s6", "group": "Ungrouped variables"}, "b1": {"templateType": "anything", "definition": "if(a*b2=a1*b,b2+1,b2)", "description": "", "name": "b1", "group": "Ungrouped variables"}, "that": {"templateType": "anything", "definition": "lcm(abs(b),abs(b1))/abs(b1)", "description": "", "name": "that", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "definition": "sb*random(1..9)", "description": "", "name": "b", "group": "Ungrouped variables"}, "s1": 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"contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Roz Wyatt-Millington", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3732/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Roz Wyatt-Millington", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3732/"}]}