// Numbas version: finer_feedback_settings
{"name": "Linear Simultaneous Equations Brunel", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image_aNW76BS.png", "image_aNW76BS.png"], ["question-resources/image_Y7v4ys8.png", "image_Y7v4ys8.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Linear Simultaneous Equations Brunel", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "", "advice": "<p>There are several ways to solve linear simultaneous equations, here we will focus on equalling the coefficients of $x$ and then subtracting the equations.</p>\n<p>To get the same coefficient of $x$ in both equations we can multiply the first by $\\simplify{{b1}}$ and the second by $\\simplify{{a1}}$:</p>\n<p>\\[\\simplify{{a1}{b1}x+{a2}{b1}y={a3}{b1}} \\quad \\text{and} \\quad \\simplify{{b1}{a1}x+{b2}{a1}y={b3}{a1}}\\]</p>\n<p>Subtracting the second from the first gives:</p>\n<p>\\[ \\simplify{({a2}{b1}-{b2}{a1})y=({a3}{b1}-{b3}{a1})}\\]</p>\n<p>Dividing through by $\\simplify{{a2}{b1}-{b2}{a1}}$ gives:</p>\n<p>\\[y=\\simplify{{y}}\\]</p>\n<p>Subbing this value of $y$ into either of the original equations gives:</p>\n<p>\\[x= \\simplify{{x}}\\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(-10..10 except [0])", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(-10..10 except [0,a1])", "description": "", "templateType": "anything", "can_override": false}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "a1*x+a2*y", "description": "", "templateType": "anything", 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"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>Solve the following simultaneous equations:</p>\n<p style=\"text-align: center;\">\\[ \\simplify{{a1}x+{a2}y={a3}}\\] \\[\\simplify{{b1}x+{b2}y={b3}}\\]</p>\n<p style=\"text-align: left;\">$x =$ [[0]]</p>\n<p style=\"text-align: left;\">$y =$ [[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "x", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x}", "maxValue": "{x}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "y", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{y}", "maxValue": "{y}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": 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