// Numbas version: exam_results_page_options
{"name": "Sistema de Ecuaciones no Lineal (3).jk", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [{"name": "Unnamed group", "variables": ["m", "n", "p"]}], "preamble": {"js": "", "css": ""}, "statement": "<p>Resolver el siguiente sistema de Ecuaciones no Lineal:</p>\n<p>\\[\\begin{eqnarray*}\\simplify{{y}}&amp;=&amp;\\simplify{x^2+{a}x+{a*b-c}}\\\\\\\\\\simplify{{y}}&amp;=&amp;\\simplify{-{b}x-{c}}\\end{eqnarray*}\\]</p>\n<p></p>", "ungrouped_variables": ["a", "b", "c", "a1", "b1", "c1", "d1", "f1", "g1", "h1", "a2", "b2", "c2", "d2", "f2", "g2", "h2", "d"], "name": "Sistema de Ecuaciones no Lineal (3).jk", "functions": {}, "metadata": {"description": "<p>Shows how to define variables to stop degenerate examples.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {"std": ["All", "fractionnumbers"]}, "parts": [{"scripts": {}, "gaps": [{"scripts": {}, "checkvariablenames": false, "checkingtype": "absdiff", "showFeedbackIcon": true, "variableReplacements": [], "marks": 1, "expectedvariablenames": [], "showCorrectAnswer": true, "checkingaccuracy": 0.001, "answersimplification": "Std", "showpreview": true, "notallowed": {"partialCredit": 0, "strings": ["."], "showStrings": false, "message": "<p>Input your answer as a fraction and not a decimal.</p>"}, "vsetrange": [0, 1], "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{-a}", "vsetrangepoints": 5}, {"scripts": {}, "checkvariablenames": false, "checkingtype": "absdiff", "showFeedbackIcon": true, "variableReplacements": [], "marks": 1, "expectedvariablenames": [], "showCorrectAnswer": true, "checkingaccuracy": 0.001, "answersimplification": "Std", "showpreview": true, "notallowed": {"partialCredit": 0, "strings": ["."], "showStrings": false, "message": "<p>Input your answer as a fraction and not as a decimal.</p>"}, "vsetrange": [0, 1], "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{-b}", "vsetrangepoints": 5}, {"scripts": {}, "checkvariablenames": false, "checkingtype": "absdiff", "showFeedbackIcon": true, "variableReplacements": [], "marks": 1, "expectedvariablenames": [], "showCorrectAnswer": true, "checkingaccuracy": 0.001, "answersimplification": "Std", "showpreview": true, "notallowed": {"partialCredit": 0, "strings": ["."], "showStrings": false, "message": "<p>Input your answer as a fraction and not as a decimal.</p>"}, "vsetrange": [0, 1], "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{(a*b)-c}", "vsetrangepoints": 5}, {"scripts": {}, "checkvariablenames": false, "checkingtype": "absdiff", "showFeedbackIcon": true, "variableReplacements": [], "marks": 1, "expectedvariablenames": [], "showCorrectAnswer": true, "checkingaccuracy": 0.001, "answersimplification": "Std", "showpreview": true, "notallowed": {"partialCredit": 0, "strings": ["."], "showStrings": false, "message": "<p>Input your answer as a fraction and not as a decimal.</p>"}, "vsetrange": [0, 1], "type": "jme", "variableReplacementStrategy": "originalfirst", "answer": "{(b*b)-c}", "vsetrangepoints": 5}], "showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "prompt": "<p><strong>Observaci&oacute;n:</strong>&nbsp;Para ingresar su respuesta como pares ordenados, h&aacute;galo con la siguiente condici&oacute;n: $\\,x_1&lt;x_2$</p>\n<p>$x_1=$&nbsp;[[0]]&nbsp;, $y_1=$&nbsp;[[2]]</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; y</p>\n<p>$x_2=$&nbsp;[[1]] ,&nbsp;$y_2=$ [[3]]</p>\n<p></p>\n<p></p>"}], "extensions": [], "tags": [], "advice": "<p>Igualemos las ecuaciones y ordenemos:</p>\n<p>\\begin{align}<br/>\\simplify{x^2+{a}x+{a*b-c}}=&amp;\\,\\simplify{-{b}x-{c}}<br/>\\end{align}</p>\n<p>\\begin{align}<br/>\\simplify{x^2+{a+b}x+{a*b}}=&amp;\\,\\simplify{0}<br/>\\end{align}</p>\n<p>Factoricemos y resolvamos:</p>\n<p>\\begin{align}<br/>(\\simplify{(x+{a})})(\\simplify{x+{b}})=&amp;\\simplify{0}<br/>\\end{align}</p>\n<p>\\[\\simplify{(x+{a}={0})} \\,\\,\\,\\,;\\,\\,\\,&nbsp;\\simplify{(x+{b}={0})} \\]</p>\n<p>\\[\\simplify{(x_1={-a})} \\,\\,\\,\\,;\\,\\,\\,&nbsp;\\simplify{(x_2={-b})} \\]</p>\n<p></p>\n<p>Ahora para $\\simplify{(x_1={-a})}$, debemos encontrar su respectivo valor de $\\,\\,y_1$. Para eso reemplazanos en la segunda ecuaci&oacute;n del sistema inicial:</p>\n<p>\\begin{align}<br/>\\simplify{y}=&amp;\\,\\simplify{-{b}x-{c}} \\\\&nbsp;<br/>\\simplify{y_1}=&amp;\\,\\simplify[!collectnumbers]{-{b}*-{a}-{c}}&nbsp;\\\\<br/>\\simplify{y_1}=&amp;\\,\\simplify{-{b}{-a}-{c}}<br/>\\end{align}</p>\n<p>Nuestra primera soluci&oacute;n es el par ordenado:</p>\n<p>\\begin{align}&nbsp;<br/>{(x_1,y_1)}=&amp;\\,(\\simplify{{-a}},\\simplify{-{b}{-a}-{c}})<br/>\\end{align}</p>\n<p>Para $\\simplify{(x_2={-b})}$, debemos encontrar su respectivo valor de $\\,\\,y_2$.&nbsp;Volvemos a reemplazar&nbsp;en la segunda ecuaci&oacute;n del sistema inicial:</p>\n<p>\\begin{align}<br/>\\simplify{y}=&amp;\\,\\simplify{-{b}x-{c}} \\\\&nbsp;<br/>\\simplify{y_2}=&amp;\\,\\simplify[!collectnumbers]{-{b}*-{b}-{c}}&nbsp;\\\\<br/>\\simplify{y_1}=&amp;\\,\\simplify{-{b}{-b}-{c}}<br/>\\end{align}</p>\n<p>La segunda&nbsp;soluci&oacute;n es el par ordenado:</p>\n<p>\\begin{align}&nbsp;<br/>{(x_2,y_2)}=&amp;\\,(\\simplify{{-b}},\\simplify{-{b}{-b}-{c}})<br/>\\end{align}</p>\n<p>Finalmente las soluciones&nbsp;del&nbsp;sistema son:</p>\n<p>\\[{(x_1,y_1)}=(\\simplify{{-a}},\\simplify{-{b}{-a}-{c}})&nbsp;\\,\\,\\,\\, \\text{y}\\,\\,\\, {(x_2,y_2)}=(\\simplify{{-b}},\\simplify{-{b}{-b}-{c}}) \\]</p>\n<p></p>", "variables": {"a1": {"name": "a1", "definition": "random(2..3)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "h1": {"name": "h1", "definition": "random(-3..3)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "n": {"name": "n", "definition": "lcm(c2,g2)", "templateType": "anything", "group": "Unnamed group", "description": ""}, "f1": {"name": "f1", "definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "c1": {"name": "c1", "definition": "random(2..6 except [5,a1,2a1,3a1])", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "d": {"name": "d", "definition": "abs(d1)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "f2": {"name": "f2", "definition": "random(-3..3 except 0)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "a": {"name": "a", "definition": "random(-7..7 except [0,-1,1])", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "a2": {"name": "a2", "definition": "random(2,3)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "c2": {"name": "c2", "definition": "random([2,3,4,6] except [a2,2a2,3a2])", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "d2": {"name": "d2", "definition": "-d1", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "p": {"name": "p", "definition": "lcm((m*d)/g1,(n*d)/g2)", "templateType": "anything", "group": "Unnamed group", "description": ""}, "g1": {"name": "g1", "definition": "random(2..5 except [d1,2d1,-d1,-2d1])", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "c": {"name": "c", "definition": "random(a,b)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "b1": {"name": "b1", "definition": "random(-3..3 except 0)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "h2": {"name": "h2", "definition": "random(-2..2 except 0)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "g2": {"name": "g2", "definition": "random(2..5 except [-d2,-2d2,d2,2d2,c2])", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "b2": {"name": "b2", "definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "m": {"name": "m", "definition": "lcm(c1,g1)", "templateType": "anything", "group": "Unnamed group", "description": ""}, "b": {"name": "b", "definition": "a-random(1..7 except abs(a))", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "d1": {"name": "d1", "definition": "random(-3,-2,2,3)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}}, "type": "question", "contributors": [{"name": "Jos Klenner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/84/"}]}]}], "contributors": [{"name": "Jos Klenner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/84/"}]}