// Numbas version: exam_results_page_options {"name": "Sistema de Ecuaciones no Lineal (4)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "statement": "

Resolver el siguiente sistema de Ecuaciones no Lineal:

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\$\\begin{eqnarray*}\\simplify{(x^2)-{b^2}(y^2)}&=&\\simplify{{c}}\\\\\\\\\\simplify{x-{b}*y}&=&\\simplify{{d}}\\end{eqnarray*}\$

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", "rulesets": {"std": ["All", "fractionnumbers"]}, "advice": "

Resolvamos por sustitución. Para eso despejemos  $x$ de la segunda ecuación y reemplacemos en la primera:

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\\begin{align}
\\simplify{x-{b}*y}=&\\,\\simplify{{d}} \\\\\\\\
\\simplify{x}=&\\,\\simplify[!collectnumbers]{{d}+{b}y}
\\end{align}

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Reemplazando  $x$   en la primera ecuación:

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\\begin{align}
\\simplify{x^2-{b^2}y^2}=&\\,\\simplify{{c}} \\\\\\\\
\\simplify[!collectnumbers]{({d}+{b}*y)^2-{b^2}*y^2}=&\\,\\simplify{{c}}
\\end{align}

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Desarrollando y resolviendo:

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\\begin{align}
\\simplify[!collectnumbers]{{d2}+{d3}*y+{b2}y^2-{b^2}*y^2}=&\\,\\simplify{{c}} \\\\\\\\
\\simplify{{d2}+2{d}*{b}*y}=&\\,\\simplify{{c}} \\\\\\\\
\\simplify{y}=&\\,\\simplify{({c}-{d2})/(2{d}*{b})}
\\end{align}

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Ahora reemplazamos el valor de ${y}=\\simplify{({c}-{d2})/(2*{d}*{b})}$ en la ecuación despejada del primer paso, para obtener el valor de  $x$

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\\begin{align}
\\simplify{x}=&\\,\\simplify[!collectnumbers]{{d}+{b}y} \\\\\\\\
{x}=&\\,\\simplify{{d}}+\\simplify{{b}}\\cdot\\simplify[std]{{({c}-{d2})/(2{d}*{b})}} \\\\\\\\
{x}=&\\,\\simplify[std]{{d}+{b}{{({c}-{d2})/(2{d}*{b})}}}
\\end{align}

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Finalmente la solución del sistema es:

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\${(x,y)}=\\left(\\simplify[std]{{d}+{b}{{({c}-{d2})/(2{d}*{b})}}},\\simplify{({c}-{d2})/(2{d}*{b})}\\right)\$

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", "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", "d", "d2", "d3", "b2"], "parts": [{"variableReplacements": [], "prompt": "

Ingrese su respuesta como números enteros o bien fracciones.

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$x=$ [[0]] , $y=$ [[1]]

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