// Numbas version: finer_feedback_settings
{"name": "Simultaneous equations by substitution 2 with parts", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Simultaneous equations by substitution 2 with parts", "tags": [], "metadata": {"description": "<p>Straightforward solving linear equations question</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Solve the pair of simulatenous equations by working through parts a) to d)</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>", "advice": "<p>We are going to solve for $x$ first. To do this, we need to eliminate $y$ from the equations.</p>\n<p>We start by rearranging equation (1)&nbsp;like so:</p>\n<p>$\\simplify{y = 1/{n2}*({ans1}-{n1}*x)}$</p>\n<p>$\\simplify{{n3}*x + {n4}/{n2}({ans1}-{n1}*x) = {ans2}}$</p>\n<p>$\\simplify{({n3}-{n1}*{n4}/{n2})*x + {n4}*{ans1}/{n2} = {ans2}}$</p>\n<p>$\\simplify{x=({n4}*{ans1}-{n2}*{ans2})/({n1}*{n4}-{n3}*{n2})}$</p>\n<p>Substitute the value of x back into equation (1) to find</p>\n<p>$\\simplify{y=({ans1}*{n3}-{n1}*{ans2})/({n2}*{n3}-{n1}*{n4})}$</p>\n<p></p>", "rulesets": {}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-10..10 except 0 except a)", "description": "", "templateType": "anything"}, "ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "{n1}*{a} + {n2}*{b}", "description": "", "templateType": "anything"}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "{n3}*{a}+{n4}*{b}", "description": "", "templateType": "anything"}, "ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "{ans1}*{n3} -  {ans2}*{n1}", "description": "", "templateType": "anything"}, "yCoef": {"name": "yCoef", "group": "Ungrouped variables", "definition": "{n3}*{n2} - {n1}*{n4}", "description": "", "templateType": "anything"}, "n1": {"name": "n1", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything"}, "n2": {"name": "n2", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything"}, "n3": {"name": "n3", "group": "Ungrouped variables", "definition": "random(-10..10 except 0 except n1)", "description": "", "templateType": "anything"}, "n4": {"name": "n4", "group": "Ungrouped variables", "definition": "random(-10..10 except 0 except n2)", "description": "", "templateType": "anything"}, "n5": {"name": "n5", "group": "Ungrouped variables", "definition": "{ans2}- {n4}*{ans1}/{n2}", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "ans1", "ans2", "ans3", "yCoef", "n1", "n2", "n3", "n4", "n5"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>We are going to solve for $x$ first. To do this, we need to eliminate $y$ from the equations.</p>\n<p>We start by rearranging equation (1)&nbsp;like so:</p>\n<p>$y =&nbsp;$[[0]]&nbsp; &nbsp; &nbsp; &nbsp;(3)</p>\n<p></p>\n<p></p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "1/{n2}*({ans1}-{n1}*x)", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Substitute equation (3) into equation (2) to give:</p>\n<p>[[0]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{{n3}*x + {n4}/{n2}({ans1}-{n1}*x) = {ans2}}", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Solve this linear equation to give &nbsp;</p>\n<p>$x = $[[0]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({n4}*{ans1}-{n2}*{ans2})/({n1}*{n4}-{n3}*{n2})", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Substitute the value of x back into equation (1) to find</p>\n<p>$y = $[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({ans1}*{n3}-{n1}*{ans2})/({n2}*{n3}-{n1}*{n4})", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}, {"name": "Susan McGlynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2148/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}, {"name": "Susan McGlynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2148/"}]}