// Numbas version: exam_results_page_options
{"name": "Ioannis's copy of Lois's copy of Simultaneous linear equations (variables)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "statement": "<p>Solve:</p>\n<p>\\[\\begin{eqnarray*} \\simplify{{a}x+{b}y}&amp;=&amp;\\var{c}\\\\\\\\\\simplify{{a1}x+{b1}y}&amp;=&amp;\\var{c1}\\end{eqnarray*}\\]</p>", "functions": {}, "ungrouped_variables": ["a", "c", "b", "a1", "b1", "c1"], "rulesets": {"std": ["All", "fractionnumbers"]}, "extensions": [], "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Shows how to define variables to stop degenerate examples.</p>"}, "name": "Ioannis's copy of Lois's copy of Simultaneous linear equations (variables)", "parts": [{"marks": 0, "scripts": {}, "variableReplacements": [], "gaps": [{"checkingType": "absdiff", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "vsetRangePoints": 5, "checkVariableNames": false, "answerSimplification": "Std", "answer": "{b1*c-b*c1}/{a*b1-a1*b}", "expectedVariableNames": [], "scripts": {}, "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "failureRate": 1, "type": "jme", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "marks": "3", "variableReplacementStrategy": "originalfirst", "notallowed": {"showStrings": false, "partialCredit": 0, "message": "<p>Input your answer as a fraction and not a decimal.</p>", "strings": ["."]}, "unitTests": []}, {"checkingType": "absdiff", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "showPreview": true, "vsetRangePoints": 5, "checkVariableNames": false, "answerSimplification": "Std", "answer": "{-c*a1+c1*a}/{a*b1-a1*b}", "expectedVariableNames": [], "scripts": {}, "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "failureRate": 1, "type": "jme", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "marks": "3", "variableReplacementStrategy": "originalfirst", "notallowed": {"showStrings": false, "partialCredit": 0, "message": "<p>Input your answer as a fraction and not as a decimal.</p>", "strings": ["."]}, "unitTests": []}], "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "gapfill", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "sortAnswers": false, "prompt": "<p>$x=$&nbsp;[[0]]</p>\n<p>$y=$&nbsp;[[1]]</p>\n<p>Input your answers as fractions (use the '/' key) and not as decimals.</p>", "variableReplacementStrategy": "originalfirst", "unitTests": []}], "advice": "<p>A general method is to make the coefficients of either $x$ or $y$ equal by multiplying one or both equations by a constant.</p>\n<p>You can then add or subtract the resulting equations to get an equation in just $x$ or $y$, which you can solve.</p>\n<p>The value of the other variable can be found by substitution into one of the original equations.</p>\n<p>For more explanation, look for the relevant resource \"Simultaneous Linear Equations\" in the <a href=\"https://moodle.uel.ac.uk/mod/page/view.php?id=672367\" target=\"_blank\" rel=\"noopener noreferrer\">Algebra - Equations</a> section of our <a href=\"https://moodle.uel.ac.uk/course/view.php?id=24176\" target=\"_blank\" rel=\"noopener noreferrer\">Maths Study Skills</a> page.</p>", "preamble": {"js": "", "css": ""}, "variables": {"b1": {"definition": "random(2..6 except[round(a1*b/a), -b, b])", "group": "Ungrouped variables", "name": "b1", "description": "", "templateType": "anything"}, "c1": {"definition": "random(1..5)", "group": "Ungrouped variables", "name": "c1", "description": "", "templateType": "anything"}, "a1": {"definition": "random(1..5 except a)", "group": "Ungrouped variables", "name": "a1", "description": "", "templateType": "anything"}, "b": {"definition": "random(-5..5 except [0,1,-1, a])", "group": "Ungrouped variables", "name": "b", "description": "", "templateType": "anything"}, "c": {"definition": "random(1..5)", "group": "Ungrouped variables", "name": "c", "description": "", "templateType": "anything"}, "a": {"definition": "random(1..5)", "group": "Ungrouped variables", "name": "a", "description": "", "templateType": "anything"}}, "type": "question", "contributors": [{"name": "Ioannis Lignos", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/757/"}]}]}], "contributors": [{"name": "Ioannis Lignos", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/757/"}]}