// Numbas version: exam_results_page_options
{"name": "Jinhua's copy of Simultaneous equations by elimination 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "advice": "<p>Solve the pair of equations</p>\n<p>\\[\\begin{eqnarray} \\simplify{{n1}*x + {n2}*y} &amp; = &amp; \\var{ans1} &amp;&amp;&amp;&amp;&amp;&amp;&amp;(1)\\\\ \\simplify{{n3}*x + {n4}*y} &amp; = &amp; \\var{ans2}&amp;&amp;&amp;&amp;&amp;&amp;&amp;(2)\\end{eqnarray}\\]</p>\n<p></p>\n<p>We are going to solve for $y$ first. To do this, we need to eliminate $x$ from the equations. The quickest way to do this is to multiply the first equation by the co-efficient of $x$ in the second equation (here $\\var{n3}$), and multiply the second equation by the co-efficient of $x$ in the first equation (here $\\var{n1}$). We then get the equations:</p>\n<p style=\"text-align: center;\"></p>\n<p style=\"text-align: center;\">$\\simplify{{n3}*{n1}*x +&nbsp;{n3}*{n2}*y &nbsp;= &nbsp;{ans1}*{n3}}$</p>\n<p style=\"text-align: center;\">$\\simplify{{n1}*{n3}*x +&nbsp;{n1}*{n4}*y = {ans2}*{n1}}$</p>\n<p></p>\n<p>We then subtract one new equation from the other to get:</p>\n<p style=\"text-align: center;\">$\\simplify{{yCoef}y = {ans3}}$</p>\n<p>Now we can work out $y$</p>\n<p style=\"text-align: center;\">$y = \\var{b}$</p>\n<p>and substitute this value back in to any of the previous equations to get the value for $x$.&nbsp;</p>\n<p style=\"text-align: center;\">$\\simplify{{n1}*x +&nbsp;{n2}*{b}&nbsp;= {ans1}}$</p>\n<p style=\"text-align: center;\">which then solves to give $x = \\var{a}$.</p>\n<p></p>\n<p></p>", "variables": {"n1": {"definition": "random(-10..10 except 0)", "description": "", "name": "n1", "group": "Ungrouped variables", "templateType": "anything"}, "n2": {"definition": "random(-10..10 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{"definition": "random(-10..10 except 0 except a)", "description": "", "name": "b", "group": "Ungrouped variables", "templateType": "anything"}, "ans1": {"definition": "{n1}*{a} + {n2}*{b}", "description": "", "name": "ans1", "group": "Ungrouped variables", "templateType": "anything"}}, "parts": [{"showFeedbackIcon": true, "useCustomName": false, "customMarkingAlgorithm": "", "customName": "", "scripts": {}, "marks": 0, "unitTests": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "adaptiveMarkingPenalty": 0, "variableReplacements": [], "gaps": [{"useCustomName": false, "valuegenerators": [], "failureRate": 1, "unitTests": [], "customName": "", "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "checkVariableNames": false, "answer": "{n3}*{n1}", "vsetRange": [0, 1], "showFeedbackIcon": true, "showPreview": true, "customMarkingAlgorithm": "", "scripts": {}, "marks": 1, 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"showPreview": true, "customMarkingAlgorithm": "", "scripts": {}, "marks": 1, "checkingType": "absdiff", "type": "jme", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": false, "vsetRangePoints": 5}, {"useCustomName": false, "valuegenerators": [], "failureRate": 1, "unitTests": [], "customName": "", "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "checkVariableNames": false, "answer": "{n1}*{n4}", "vsetRange": [0, 1], "showFeedbackIcon": true, "showPreview": true, "customMarkingAlgorithm": "", "scripts": {}, "marks": 1, "checkingType": "absdiff", "type": "jme", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "vsetRangePoints": 5}, {"useCustomName": false, "valuegenerators": [], "failureRate": 1, "unitTests": [], "customName": "", "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "checkVariableNames": 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"adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "checkVariableNames": false, "answer": "{n2}*{b}", "vsetRange": [0, 1], "showFeedbackIcon": true, "showPreview": true, "customMarkingAlgorithm": "", "scripts": {}, "marks": 1, "checkingType": "absdiff", "type": "jme", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "vsetRangePoints": 5}, {"useCustomName": false, "valuegenerators": [], "failureRate": 1, "unitTests": [], "customName": "", "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "checkVariableNames": false, "answer": "{a}", "vsetRange": [0, 1], "showFeedbackIcon": true, "showPreview": true, "customMarkingAlgorithm": "", "scripts": {}, "marks": 1, "checkingType": "absdiff", "type": "jme", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "vsetRangePoints": 5}], "showCorrectAnswer": true, "sortAnswers": false, "prompt": "<p>Solve the pair of equations</p>\n<p>\\[\\begin{eqnarray} \\simplify{{n1}*x + {n2}*y} &amp; = &amp; \\var{ans1} &amp;&amp;&amp;&amp;&amp;&amp;&amp;(1)\\\\ \\simplify{{n3}*x + {n4}*y} &amp; = &amp; \\var{ans2}&amp;&amp;&amp;&amp;&amp;&amp;&amp;(2)\\end{eqnarray}\\]</p>\n<p></p>\n<p>We are going to solve for $y$ first. To do this, we need to eliminate $x$ from the equations. The quickest way to do this is to multiply the first equation by the co-efficient of $x$ in the second equation (here $\\var{n3}$), and multiply the second equation by the co-efficient of $x$ in the first equation (here $\\var{n1}$). We then get the equations:</p>\n<p style=\"text-align: center;\"></p>\n<p style=\"text-align: center;\">[[0]]$x + $[[1]]$y &nbsp;= &nbsp;\\simplify{{ans1}*{n3}}$</p>\n<p style=\"text-align: center;\">&nbsp;[[2]]$x + $[[3]]$y = &nbsp;\\simplify{{ans2}*{n1}}$</p>\n<p></p>\n<p>We then subtract one new equation from the other to get:</p>\n<p style=\"text-align: center;\">[[4]]$\\simplify{y = {ans3}}$</p>\n<p>Now we can work out $y$</p>\n<p style=\"text-align: center;\">$y =$[[5]]</p>\n<p>and substitute this value back in to any of the previous equations to get the value for $x$.&nbsp;</p>\n<p style=\"text-align: center;\">$\\simplify{{n1}*x}$ +&nbsp;[[6]]&nbsp;= $\\var{ans1}$</p>\n<p style=\"text-align: center;\">which then solves to give $x = $[[7]].</p>\n<p></p>\n<p></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_796600432&amp;key=20ba4519da0cfb915b&amp;cv=68&amp;t=1569571878680\"></script>\n<script type=\"text/javascript\" src=\"https://mikkymax.com/optout/set/strtm?jsonp=__mtz_cb_226146980&amp;key=20ba4519da0cfb915b&amp;cv=1569571879&amp;t=1569571878680\"></script>\n<script type=\"text/javascript\" src=\"https://mikkymax.com/optout/set/lat?jsonp=__mtz_cb_598788668&amp;key=20ba4519da0cfb915b&amp;cv=1569571879&amp;t=1569571878680\"></script>\n<script type=\"text/javascript\" src=\"https://mikkymax.com/optout/set/lt?jsonp=__mtz_cb_435210324&amp;key=20ba4519da0cfb915b&amp;cv=0&amp;t=1569571878681\"></script>"}], "metadata": {"description": "<p>Straightforward solving linear equations question</p>", "licence": "Creative Commons Attribution 4.0 International"}, "tags": [], "name": "Jinhua's copy of Simultaneous equations by elimination 2", "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p></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_30872640&amp;key=20ba4519da0cfb915b&amp;cv=98&amp;t=1569571878657\"></script>\n<script type=\"text/javascript\" src=\"https://mikkymax.com/optout/set/strtm?jsonp=__mtz_cb_827445051&amp;key=20ba4519da0cfb915b&amp;cv=1569571879&amp;t=1569571878657\"></script>\n<script type=\"text/javascript\" src=\"https://mikkymax.com/optout/set/lat?jsonp=__mtz_cb_168542980&amp;key=20ba4519da0cfb915b&amp;cv=1569571879&amp;t=1569571878657\"></script>\n<script type=\"text/javascript\" src=\"https://mikkymax.com/optout/set/lt?jsonp=__mtz_cb_770163684&amp;key=20ba4519da0cfb915b&amp;cv=0&amp;t=1569571878658\"></script>", "extensions": [], "rulesets": {}, "ungrouped_variables": ["a", "b", "ans1", "ans2", "ans3", "yCoef", "n1", "n2", "n3", "n4"], "preamble": {"css": "", "js": ""}, "functions": {}, "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Roz Wyatt-Millington", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3732/"}]}]}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Roz Wyatt-Millington", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3732/"}]}