Shows how to define variables to stop degenerate examples.
", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "Resolvamos el sistema por el método de Reducción.
\nMultiplique la primera ecuación por $\\var{b1}$ y la segunda ecuación por $\\var{b}$ de modo que ambas ecuaciones tengan el mismo coeficiente en la variable $y$:
\n\\begin{align}
\\simplify{{a*b1}x+{b*b1}y} &= \\var{c*b1} \\\\
\\simplify{{a1*b}x+{b1*b}y} &= \\var{c1*b}
\\end{align}
Ahora la primera ecuación se resta con la segunda:
\n\\begin{align}
\\simplify{{a*b1}x+{b*b1}y}-(\\simplify{{a1*b}x+{b1*b}y}) &= \\var{c*b1}-(\\var{c1*b})
\\end{align}
\\[ \\simplify[std]{{a*b1-a1*b}x} = \\var{c*b1-c1*b} \\]
\nAsí:
\n\\[x = \\simplify[std]{{(c*b1-c1*b)/(a*b1-a1*b)}}\\]
\nSustituya este valor de $x=\\simplify[std]{{(c*b1-c1*b)/(a*b1-a1*b)}}$ en la primera ecuación y resuelva para obtener $y$:
\n\\begin{align}
\\simplify{{a}x+{b}y}&=\\var{c} \\\\\\\\
\\simplify[std]{({a}){(c*b1-c1*b)/(a*b1-a1*b)} + {b}y} &= \\var{c} \\\\\\\\
\\simplify[std]{{b}y} &= \\simplify[std]{{c}-{a*(c*b1-c1*b)/(a*b1-a1*b)}} \\\\\\\\
y &= \\simplify[std]{{(c-a*(c*b1-c1*b)/(a*b1-a1*b))/b}}
\\end{align}
Input your answer as a fraction and not a decimal.
", "partialCredit": 0, "strings": ["."], "showStrings": false}, "showpreview": true, "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "answersimplification": "Std", "expectedvariablenames": [], "checkvariablenames": false, "type": "jme", "marks": 1, "answer": "{b1*c-b*c1}/{a*b1-a1*b}"}, {"showCorrectAnswer": true, "vsetrange": [0, 1], "scripts": {}, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "notallowed": {"message": "Input your answer as a fraction and not as a decimal.
", "partialCredit": 0, "strings": ["."], "showStrings": false}, "showpreview": true, "checkingtype": "absdiff", "variableReplacements": [], "checkingaccuracy": 0.001, "answersimplification": "Std", "expectedvariablenames": [], "checkvariablenames": false, "type": "jme", "marks": 1, "answer": "{-c*a1+c1*a}/{a*b1-a1*b}"}], "prompt": "$x=$ [[0]]
\n$y=$ [[1]]
\nIngrese su respuesta como números enteros o bien fracciones.
", "showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst"}], "variables": {"c1": {"templateType": "anything", "group": "Ungrouped variables", "name": "c1", "definition": "random(1..5)", "description": ""}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "name": "a1", "definition": "random(1..9)", "description": ""}, "a": {"templateType": "anything", "group": "Ungrouped variables", "name": "a", "definition": "random(1..9)", "description": ""}, "b1": {"templateType": "anything", "group": "Ungrouped variables", "name": "b1", "definition": "random(1..9 except round(a1*b/a))", "description": ""}, "b": {"templateType": "anything", "group": "Ungrouped variables", "name": "b", "definition": "random(-9..9 except [0,a])", "description": ""}, "c": {"templateType": "anything", "group": "Ungrouped variables", "name": "c", "definition": "random(1..9)", "description": ""}}, "name": "Sistema de Ecuaciones (2x2) (1).jk", "functions": {}, "ungrouped_variables": ["a", "c", "b", "a1", "b1", "c1"], "preamble": {"css": "", "js": ""}, "statement": "Resolver el siguiente sistema de Ecuaciones Lineales:
\n\\[\\begin{eqnarray*} \\simplify{{a}x+{b}y}&=&\\var{c}\\\\\\simplify{{a1}x+{b1}y}&=&\\var{c1}\\end{eqnarray*}\\]
", "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/"}]}