// Numbas version: exam_results_page_options
{"name": "Viet'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": [{"ungrouped_variables": ["a", "b", "ans1", "ans2", "ans3", "yCoef", "n1", "n2", "n3", "n4"], "variables": {"b": {"templateType": "anything", "definition": "random(-10..10 except 0 except a)", "description": "", "name": "b", "group": "Ungrouped variables"}, "ans3": {"templateType": "anything", "definition": "{ans1}*{n3} -  {ans2}*{n1}", "description": "", "name": "ans3", "group": "Ungrouped variables"}, "ans2": {"templateType": "anything", "definition": "{n3}*{a}+{n4}*{b}", "description": "", "name": "ans2", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "definition": "random(-10..10 except 0)", "description": "", "name": "a", "group": "Ungrouped variables"}, "n1": {"templateType": "anything", "definition": "random(-10..10 except 0)", "description": "", "name": "n1", "group": "Ungrouped variables"}, "n3": {"templateType": "anything", "definition": "random(-10..10 except 0 except n1)", "description": "", "name": "n3", "group": "Ungrouped variables"}, "ans1": {"templateType": "anything", "definition": "{n1}*{a} + {n2}*{b}", "description": "", "name": "ans1", "group": "Ungrouped variables"}, "yCoef": {"templateType": "anything", "definition": "{n3}*{n2} - {n1}*{n4}", "description": "", "name": "yCoef", "group": "Ungrouped variables"}, "n4": {"templateType": "anything", "definition": "random(-10..10 except 0 except n2)", "description": "", "name": "n4", "group": "Ungrouped variables"}, "n2": {"templateType": "anything", "definition": "random(-10..10 except 0)", "description": "", "name": "n2", "group": "Ungrouped variables"}}, "statement": "", "extensions": [], "tags": [], "parts": [{"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>", "useCustomName": false, "type": "gapfill", "extendBaseMarkingAlgorithm": true, "sortAnswers": false, "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "marks": 0, 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"variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "customName": "", "checkingType": "absdiff", "checkVariableNames": false}, {"checkingAccuracy": 0.001, "useCustomName": false, "type": "jme", "extendBaseMarkingAlgorithm": true, "failureRate": 1, "showCorrectAnswer": false, "variableReplacements": [], "answer": "{n1}*{n3}", "showPreview": true, "showFeedbackIcon": true, "valuegenerators": [], "vsetRangePoints": 5, "scripts": {}, "marks": 1, "unitTests": [], "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "customName": "", "checkingType": "absdiff", "checkVariableNames": false}, {"checkingAccuracy": 0.001, "useCustomName": false, "type": "jme", "extendBaseMarkingAlgorithm": true, "failureRate": 1, "showCorrectAnswer": true, "variableReplacements": [], "answer": "{n1}*{n4}", "showPreview": true, "showFeedbackIcon": true, "valuegenerators": [], "vsetRangePoints": 5, "scripts": {}, "marks": 1, "unitTests": [], "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "customName": "", "checkingType": "absdiff", "checkVariableNames": false}, {"checkingAccuracy": 0.001, "useCustomName": false, "type": "jme", "extendBaseMarkingAlgorithm": true, "failureRate": 1, "showCorrectAnswer": true, "variableReplacements": [], "answer": "{yCoef}", "showPreview": true, "showFeedbackIcon": true, "valuegenerators": [], "vsetRangePoints": 5, "scripts": {}, "marks": 1, "unitTests": [], "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "customName": "", "checkingType": "absdiff", "checkVariableNames": false}, {"checkingAccuracy": 0.001, "useCustomName": false, "type": "jme", "extendBaseMarkingAlgorithm": true, "failureRate": 1, "showCorrectAnswer": true, "variableReplacements": [], "answer": "{b}", "showPreview": true, "showFeedbackIcon": true, "valuegenerators": [], "vsetRangePoints": 5, "scripts": {}, "marks": 1, "unitTests": [], "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "customName": "", "checkingType": "absdiff", "checkVariableNames": false}, {"checkingAccuracy": 0.001, "useCustomName": false, "type": "jme", "extendBaseMarkingAlgorithm": true, "failureRate": 1, "showCorrectAnswer": true, "variableReplacements": [], "answer": "{n2}*{b}", "showPreview": true, "showFeedbackIcon": true, "valuegenerators": [], "vsetRangePoints": 5, "scripts": {}, "marks": 1, "unitTests": [], "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "customName": "", "checkingType": "absdiff", "checkVariableNames": false}, {"checkingAccuracy": 0.001, "useCustomName": false, "type": "jme", "extendBaseMarkingAlgorithm": true, "failureRate": 1, "showCorrectAnswer": true, "variableReplacements": [], "answer": "{a}", "showPreview": true, "showFeedbackIcon": true, "valuegenerators": [], "vsetRangePoints": 5, "scripts": {}, "marks": 1, "unitTests": [], "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "customName": "", "checkingType": "absdiff", "checkVariableNames": false}]}], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Straightforward solving linear equations question</p>"}, "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>", "functions": {}, "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "name": "Viet's copy of Simultaneous equations by elimination 2", "rulesets": {}, "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}, {"name": "Viet Hoang", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2001/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}, {"name": "Viet Hoang", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2001/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}