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{"name": "Algebra VIII: solving simultaneous equations (equate & substitute)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"type": "question", "metadata": {"description": "<p>Straightforward solving linear equations question.</p>\n<p><em>Adapted from&nbsp;</em><strong>'Simultaneous equations by substitution 3 with parts'</strong><em> by&nbsp;</em><strong>Joshua Boddy</strong>.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans3": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "{ans1}*{n3} -  {ans2}*{n1}", "name": "ans3"}, "yCoef": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "{n3}*{n2} - {n1}*{n4}", "name": "yCoef"}, "a": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10 except 0)", "name": "a"}, "ans1": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "{n1}*{a} + {n2}*{b}", "name": "ans1"}, "b": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10 except 0 except a)", "name": "b"}, "ans2": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "{n3}*{a}+{n4}*{b}", "name": "ans2"}, "n3": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10 except 0 except n1)", "name": "n3"}, "n2": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "1", "name": "n2"}, "n1": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-10..10 except 0)", "name": "n1"}, "n4": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "1", "name": "n4"}}, "statement": "<p>Find the point of intersection of the following pair of straight lines by working through parts a) to d)</p>\n<p>\\[\\begin{eqnarray} \\simplify{{n2}*y = {ans1} - {n1}*x} &amp;&amp;&amp;&amp;&amp;&amp;&amp;(1)\\\\ \\simplify{{n4}*y = {ans2} - {n3}*x} &amp;&amp;&amp;&amp;&amp;&amp;&amp;(2)\\end{eqnarray}\\]</p>", "functions": {}, "tags": [], "extensions": [], "parts": [{"type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"type": "jme", "scripts": {}, "expectedvariablenames": [], "checkvariablenames": false, "vsetrangepoints": 5, "answersimplification": "all", "checkingtype": "absdiff", "checkingaccuracy": 0.001, "marks": 1, "answer": "{n3}-{n1}*{n4}/{n2}", "variableReplacements": [], "vsetrange": [0, 1], "showpreview": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true}], "variableReplacementStrategy": "originalfirst", "prompt": "<p>We are going to solve for $x$ first. To do this, we need to eliminate $y$ from the equations.</p>\n<p>By equating equation (1) and equation (2), we find that:</p>\n<p>[[0]]$\\simplify{x = {ans2} - {n4}*{ans1}/{n2}}$</p>\n<p></p>", "variableReplacements": []}, {"type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"type": "jme", "scripts": {}, "expectedvariablenames": [], "checkvariablenames": false, "vsetrangepoints": 5, "answersimplification": "all", "checkingtype": "absdiff", "checkingaccuracy": 0.001, "marks": 1, "answer": "({n4}*{ans1}-{n2}*{ans2})/({n1}*{n4}-{n3}*{n2})", "variableReplacements": [], "vsetrange": [0, 1], "showpreview": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true}], "variableReplacementStrategy": "originalfirst", "prompt": "<p>Solve this linear equation to give &nbsp;$x = $[[0]]</p>\n<p></p>", "variableReplacements": []}, {"type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"type": "jme", "scripts": {}, "expectedvariablenames": [], "checkvariablenames": false, "vsetrangepoints": 5, "answersimplification": "all", "checkingtype": "absdiff", "checkingaccuracy": 0.001, "marks": 1, "answer": "({ans1}*{n3}-{n1}*{ans2})/({n2}*{n3}-{n1}*{n4})", "variableReplacements": [], "vsetrange": [0, 1], "showpreview": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true}], "variableReplacementStrategy": "originalfirst", "prompt": "<p>Substitute the value of x back into equation (1) or equation (2) to find</p>\n<p>$y = $[[0]]</p>", "variableReplacements": []}], "showQuestionGroupNames": false, "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>$\\simplify{{n3}*x + {n4}/{n2}({ans1}-{n1}*x) - {ans2} = 0}$</p>\n<p>$\\simplify{({n3}-{n1}*{n4}/{n2})*x + {n4}*{ans1}/{n2} - {ans2} = 0}$</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>", "name": "Algebra VIII: solving simultaneous equations (equate & substitute)", "rulesets": {}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["a", "b", "ans1", "ans2", "ans3", "yCoef", "n1", "n2", "n3", "n4"], "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Luke Park", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/826/"}, {"name": "heike hoffmann", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2960/"}]}]}], "contributors": [{"name": "Luke Park", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/826/"}, {"name": "heike hoffmann", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2960/"}]}