// Numbas version: exam_results_page_options
{"name": "Solve a pair of simultaneous equations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"s1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "s1", "description": ""}, "aort": {"group": "Ungrouped variables", "templateType": "anything", "definition": "if(b*b1>0,'take away the equation','add the equation')", "name": "aort", "description": ""}, "b": {"group": "Ungrouped variables", "templateType": "anything", "definition": "sb*random(1..9)", "name": "b", "description": ""}, "c": {"group": "Ungrouped variables", "templateType": "anything", "definition": "sc*random(1..9)", "name": "c", "description": ""}, "sc": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "sc", "description": ""}, "sc1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "sc1", "description": ""}, "b1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "if(a*b2=a1*b,b2+1,b2)", "name": "b1", "description": ""}, "fromorto": {"group": "Ungrouped variables", "templateType": "anything", "definition": "if(b*b1>0,'from','to')", "name": "fromorto", "description": ""}, "that": {"group": "Ungrouped variables", "templateType": "anything", "definition": "lcm(abs(b),abs(b1))/abs(b1)", "name": "that", "description": ""}, "sb": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "sb", "description": ""}, "b2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)", "name": "b2", "description": ""}, "this": {"group": "Ungrouped variables", "templateType": "anything", "definition": "lcm(abs(b),abs(b1))/abs(b)", "name": "this", "description": ""}, "c1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "sc1*random(1..9)", "name": "c1", "description": ""}, "s6": {"group": "Ungrouped variables", "templateType": "anything", "definition": "if(b*b1>0,-1,1)", "name": "s6", "description": ""}, "a": {"group": "Ungrouped variables", "templateType": "anything", "definition": "sa*random(2..9)", "name": "a", "description": ""}, "a1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "switch(a2=2,random(3,5,7,9),a2=3,random(2,4,5,7),a2=4,random(3,5,7,9),a2=5,random(3,4,6,7,9),a2=6,random(4,5,7,8,9),a2=7,random(3,4,5,6,8,9),a2=8,random(3,5,6,7,9),a2=9,random(2,4,5,7,8),9)", "name": "a1", "description": ""}, "sa": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "sa", "description": ""}, "a2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "abs(a)", "name": "a2", "description": ""}}, "ungrouped_variables": ["a", "c", "b", "that", "this", "sc1", "s1", "s6", "a1", "aort", "a2", "b1", "b2", "sc", "sb", "sa", "fromorto", "c1"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Solve a pair of simultaneous equations", "showQuestionGroupNames": false, "functions": {}, "parts": [{"marks": 0, "scripts": {}, "gaps": [{"answer": "{c*b1-b*c1}/{b1*a-a1*b}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "notallowed": {"showStrings": false, "message": "<p>Input as a fraction or an integer not as a decimal</p>", "strings": ["."], "partialCredit": 0}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "answersimplification": "std", "type": "jme", "showCorrectAnswer": true, "marks": 2, "vsetrangepoints": 5}, {"answer": "{c*a1-a*c1}/{b*a1-a*b1}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "notallowed": {"showStrings": false, "message": "<p>Input as a fraction or an integer not as a decimal</p>", "strings": ["."], "partialCredit": 0}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "answersimplification": "std", "type": "jme", "showCorrectAnswer": true, "marks": 2, "vsetrangepoints": 5}], "type": "gapfill", "showCorrectAnswer": true, "steps": [{"type": "information", "prompt": "<p><iframe height=\"480\" src=\"https://player.vimeo.com/video/8174096\" frameborder=\"0\" width=\"640\" allowfullscreen=\"\" mozallowfullscreen=\"\" webkitallowfullscreen=\"\"></iframe></p>", "showCorrectAnswer": true, "scripts": {}, "marks": 0}], "prompt": "\n\t\t\t      <p>\\[ \\begin{eqnarray} \\simplify[std]{{a}x+{b}y}&amp;=&amp;\\var{c}\\\\ \\simplify[std]{{a1}x+{b1}y}&amp;=&amp;\\var{c1} \\end{eqnarray} \\]</p>\n\t\t\t        <p>$x=\\phantom{{}}$[[0]],&nbsp;$y=\\phantom{{}}$[[1]]</p>\n\t\t\t        <p>Input your answers as fractions or integers,&nbsp;<span class=\"caps\">not</span>&nbsp;as decimals.</p>\n\t\t\t        <p>See \"Show steps\" for a video that describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.</p>\n\t\t\t      \n\t\t\t", "stepsPenalty": 0}], "statement": "<p>Solve the following simultaneous equations for $x$ and $y$. Input your answers as fractions or integers,&nbsp;<span class=\"caps\">not</span> as decimals.</p>", "tags": ["ACC1012", "checked2015", "equations", "linear", "pair of linear equations", "simultaneous", "simultaneous linear equations", "solve linear equations", "solving equations", "Solving equations", "video"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n\t\t    \t\t        \t\t        \t\t        \t\t    \t\t                \t\t<p><strong>5/08/2012:</strong></p>\n\t\t    \t\t        \t\t        \t\t        \t\t    \t\t                \t\t    <p>Added more tags.</p>\n\t\t    \t\t        \t\t        \t\t        \t\t    \t\t                \t\t    <p>Added description.</p>\n\t\t    \t\t        \t\t        \t\t        \t\t    \t\t                \t\t    <p>Checked calculation. OK.</p>\n\t\t    \t\t        \t\t        \t\t        \t\t    \t\t                \n\t\t    \t\t        \t\t        \t\t        \t\t    \n\t\t    \t\t        \t\t        \t\t        \n\t\t    \t\t        \t\t        \n\t\t    \t\t        \n\t\t    \n\t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solve for $x$ and $y$: &nbsp;\\[ \\begin{eqnarray} a_1x+b_1y&amp;=&amp;c_1\\\\&nbsp; &nbsp;a_2x+b_2y&amp;=&amp;c_2&nbsp;\\end{eqnarray} \\]</p>\n<p>The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "\n\t    <p>\\[ \\begin{eqnarray} \\simplify[std]{{a}x+{b}y}&amp;=&amp;\\var{c}&amp;\\mbox{ ........(1)}\\\\ \\simplify[std]{{a1}x+{b1}y}&amp;=&amp;\\var{c1}&amp;\\mbox{ ........(2)} \\end{eqnarray} \\]<br/>To get a solution for $x$ multiply equation (1) by {this} and equation (2) by {that}</p>\n\t  <p>This gives:<br/>\\[ \\begin{eqnarray} \\simplify[std]{{a*this}x+{b*this}y}&amp;=&amp;\\var{this*c}&amp;\\mbox{ ........(3)}\\\\ \\simplify[std]{{a1*that}x+{b1*that}y}&amp;=&amp;\\var{that*c1}&amp;\\mbox{ ........(4)} \\end{eqnarray} \\] <br/>Now {aort} (4) {fromorto} equation (3) to get<br/>\\[\\simplify[std]{({a*this}+{s6*a1*that})x={this*c}+{s6*that*c1}}\\]<br/>And so we get the solution for $x$:<br/>\\[x = \\simplify{{c*b1-b*c1}/{b1*a-a1*b}}\\]<br/>Substituting this value into any of the equations (1) and (2) gives:<br/>\\[y = \\simplify{{c*a1-a*c1}/{b*a1-a*b1}}\\]<br/>You can check that these solutions are correct by seeing if they satisfy both equations (1) and (2) by substituting these values into the equations.</p>\n\t    \n\t    \n\t  \n\t  \n\t  \n\t  \n\t", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}