// Numbas version: exam_results_page_options {"name": "Sistema de Ecuaciones no Lineal (3)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "statement": "
Resolver el siguiente sistema de Ecuaciones no Lineal:
\n\\[\\begin{eqnarray*}\\simplify{{y}}&=&\\simplify{x^2+{a}x+{a*b-c}}\\\\\\\\\\simplify{{y}}&=&\\simplify{-{b}x-{c}}\\end{eqnarray*}\\]
\n", "rulesets": {"std": ["All", "fractionnumbers"]}, "advice": "Igualemos las ecuaciones y ordenemos:
\n\\begin{align}
\\simplify{x^2+{a}x+{a*b-c}}=&\\,\\simplify{-{b}x-{c}}
\\end{align}
\\begin{align}
\\simplify{x^2+{a+b}x+{a*b}}=&\\,\\simplify{0}
\\end{align}
Factoricemos y resolvamos:
\n\\begin{align}
(\\simplify{(x+{a})})(\\simplify{x+{b}})=&\\simplify{0}
\\end{align}
\\[\\simplify{(x+{a}={0})} \\,\\,\\,\\,;\\,\\,\\, \\simplify{(x+{b}={0})} \\]
\n\\[\\simplify{(x_1={-a})} \\,\\,\\,\\,;\\,\\,\\, \\simplify{(x_2={-b})} \\]
\n\nAhora para $\\simplify{(x_1={-a})}$, debemos encontrar su respectivo valor de $\\,\\,y_1$. Para eso reemplazanos en la segunda ecuación del sistema inicial:
\n\\begin{align}
\\simplify{y}=&\\,\\simplify{-{b}x-{c}} \\\\
\\simplify{y_1}=&\\,\\simplify[!collectnumbers]{-{b}*-{a}-{c}} \\\\
\\simplify{y_1}=&\\,\\simplify{-{b}{-a}-{c}}
\\end{align}
Nuestra primera solución es el par ordenado:
\n\\begin{align}
{(x_1,y_1)}=&\\,(\\simplify{{-a}},\\simplify{-{b}{-a}-{c}})
\\end{align}
Para $\\simplify{(x_2={-b})}$, debemos encontrar su respectivo valor de $\\,\\,y_2$. Volvemos a reemplazar en la segunda ecuación del sistema inicial:
\n\\begin{align}
\\simplify{y}=&\\,\\simplify{-{b}x-{c}} \\\\
\\simplify{y_2}=&\\,\\simplify[!collectnumbers]{-{b}*-{b}-{c}} \\\\
\\simplify{y_1}=&\\,\\simplify{-{b}{-b}-{c}}
\\end{align}
La segunda solución es el par ordenado:
\n\\begin{align}
{(x_2,y_2)}=&\\,(\\simplify{{-b}},\\simplify{-{b}{-b}-{c}})
\\end{align}
Finalmente las soluciones del sistema son:
\n\\[{(x_1,y_1)}=(\\simplify{{-a}},\\simplify{-{b}{-a}-{c}}) \\,\\,\\,\\, \\text{y}\\,\\,\\, {(x_2,y_2)}=(\\simplify{{-b}},\\simplify{-{b}{-b}-{c}}) \\]
\n", "extensions": [], "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Shows how to define variables to stop degenerate examples.
"}, "ungrouped_variables": ["a", "b", "c", "a1", "b1", "c1", "d1", "f1", "g1", "h1", "a2", "b2", "c2", "d2", "f2", "g2", "h2", "d"], "parts": [{"variableReplacements": [], "prompt": "Observación: Para ingresar su respuesta como pares ordenados, hágalo con la siguiente condición: $\\,x_1<x_2$
\n$x_1=$ [[0]] , $y_1=$ [[2]]
\ny
\n$x_2=$ [[1]] , $y_2=$ [[3]]
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