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