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{"name": "Q3 (simultaneous equations, solve for x and y)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "c", "a1", "b1", "c1", "ans1", "ans2", "a21", "a22", "a31", "a32", "b21", "b22", "b31", "b32", "ans21", "c21", "c22", "ans22", "ans31", "ans32", "c31", "c32"], "name": "Q3 (simultaneous equations, solve for x and y)", "tags": ["rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>Have a look at this youtube video to understand simultaneous equations better:&nbsp;<a href=\"https://www.youtube.com/watch?v=Lwto-lQzmec\">Simultaneous Equations</a></p>\n<p>To find x:</p>\n<p>$\\frac{((\\var{b} \\times \\var{c1}) - (\\var{b1} \\times \\var{c}))}{((\\var{a1} \\times \\var{b}) - (\\var{a} \\times \\var{b1}))} = \\var{ans1}$</p>\n<p>To find y:</p>\n<p>$\\frac{(\\var{c1} - (\\var{a1} \\times \\var{ans1}))}{\\var{b1}} = \\var{ans2}$</p>\n<p></p>\n<p>Parts B and C are done using the same method.</p>\n<p></p>", "rulesets": {"std": ["all"]}, "parts": [{"stepsPenalty": 0, "prompt": "<p>$\\simplify{{a}x + {b}y = {c}}$</p>\n<p>$\\simplify{{a1}x + {b1}y = {c1}}$</p>\n<p>x: &nbsp;[[0]]</p>\n<p>y: &nbsp;[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>It might be helpful to multiply each equation by 10 first to get rid of the decimals.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}+0.5", "strictPrecision": false, "minValue": "{ans1}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2} +0.5", "strictPrecision": false, "minValue": "{ans2} -0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\simplify{{a21}x + {b21}y = {c21}}$</p>\n<p>$\\simplify{{a22}x + {b22}y = {c22}}$</p>\n<p>x: &nbsp;[[0]]</p>\n<p>y: &nbsp;[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans21}+0.5", "strictPrecision": false, "minValue": "{ans21}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22} +0.5", "strictPrecision": false, "minValue": "{ans22} -0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\simplify{{a31}x + {b31}y = {c31}}$</p>\n<p>$\\simplify{{a32}x + {b32}y = {c32}}$</p>\n<p>x: &nbsp;[[0]]</p>\n<p>y: &nbsp;[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}+0.5", "strictPrecision": false, "minValue": "{ans31}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans32} +0.5", "strictPrecision": false, "minValue": "{ans32} -0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Solve for x and y:</p>\n<p><em>Correct to one decimal place!!</em></p>\n<p><em>Also make sure you do not round off too early!!!</em></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a21": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a21", "description": ""}, "a22": {"definition": "random(1..9#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a22", "description": ""}, "ans1": {"definition": "(b*c1 - b1*c)/(a1*b - a*b1) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "(c1 - a1*ans1)/(b1) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "b22": {"definition": "random(-9..9#0.1 except[a21,0])", "templateType": "anything", "group": "Ungrouped variables", "name": "b22", "description": ""}, "b21": {"definition": "random(-9..9 except [0,a21])", "templateType": "anything", "group": "Ungrouped variables", "name": "b21", "description": ""}, "b1": {"definition": "random(-9..9 except[a1,0])", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "c1": {"definition": "random(-9..9 except [0,b1,round(b1/2),round(b1/3),round(b1/4),b1*2,b1*3,b1*4,b1*1.5,b1*2.5,b1*3.5,b1*4.5,round(b1/1.5),round(b1/2.5),round(b1/3.5),round(b1/4.5)])", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "ans21": {"definition": "(b21*c22 - b22*c21)/(a22*b21 - a21*b22) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "ans22": {"definition": "(c22 - a22*ans21)/(b22) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "c31": {"definition": "random(-9..9#0.1 except [0,b31,round(b31/2),round(b31/3),round(b31/4),b31*2,b31*3,b31*4,b31*1.5,b31*2.5,b31*3.5,b31*4.5,round(b31/1.5),round(b31/2.5),round(b31/3.5),round(b31/4.5)])", "templateType": "anything", "group": "Ungrouped variables", "name": "c31", "description": ""}, "c32": {"definition": "random(-9..9#0.1 except [0,b32,round(b32/2),round(b32/3),round(b32/4),b32*2,b32*3,b32*4,b32*1.5,b32*2.5,b32*3.5,b32*4.5,round(b32/1.5),round(b32/2.5),round(b32/3.5),round(b32/4.5)])", "templateType": "anything", "group": "Ungrouped variables", "name": "c32", "description": ""}, "a32": {"definition": "random(1..9#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a32", "description": ""}, "a31": {"definition": "random(1..9#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a31", "description": ""}, "b31": {"definition": "random(-9..9#0.1 except [0,a31])", "templateType": "anything", "group": "Ungrouped variables", "name": "b31", "description": ""}, "b32": {"definition": "random(-9..9#0.1 except[b21,0])", "templateType": "anything", "group": "Ungrouped variables", "name": "b32", "description": ""}, "a1": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "b": {"definition": "random(-9..9 except [0,a])", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "ans31": {"definition": "(b31*c32 - b32*c31)/(a32*b31 - a31*b32) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "(c32 - a32*ans31)/(b32) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "a": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-9..9 except [0,b,round(b/2),round(b/3),round(b/4),b*2,b*3,b*4,b*1.5,b*2.5,b*3.5,b*4.5,round(b/1.5),round(b/2.5),round(b/3.5),round(b/4.5)])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "c21": {"definition": "random(-9..9 except [0,b21,round(b21/2),round(b21/3),round(b21/4),b21*2,b21*3,b21*4,b21*1.5,b21*2.5,b21*3.5,b21*4.5,round(b21/1.5),round(b21/2.5),round(b21/3.5),round(b21/4.5)])", "templateType": "anything", "group": "Ungrouped variables", "name": "c21", "description": ""}, "c22": {"definition": "random(-9..9#0.1 except [0,b22,round(b22/2),round(b22/3),round(b22/4),b22*2,b22*3,b22*4,b22*1.5,b22*2.5,b22*3.5,b22*4.5,round(b22/1.5),round(b22/2.5),round(b22/3.5),round(b22/4.5)])", "templateType": "anything", "group": "Ungrouped variables", "name": "c22", "description": ""}}, "metadata": {"description": "<p>Simultaneous Linear Equations</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}