Resolver el siguiente sistema de Ecuaciones no Lineal:
\n\\[\\begin{eqnarray*}\\simplify{(x^2)-{b^2}(y^2)}&=&\\simplify{{c}}\\\\\\\\\\simplify{x-{b}*y}&=&\\simplify{{d}}\\end{eqnarray*}\\]
\n", "rulesets": {"std": ["All", "fractionnumbers"]}, "advice": "Resolvamos por sustitución. Para eso despejemos $x$ de la segunda ecuación y reemplacemos en la primera:
\n\\begin{align}
\\simplify{x-{b}*y}=&\\,\\simplify{{d}} \\\\\\\\
\\simplify{x}=&\\,\\simplify[!collectnumbers]{{d}+{b}y}
\\end{align}
Reemplazando $x$ en la primera ecuación:
\n\\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}
Desarrollando y resolviendo:
\n\\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}
Ahora reemplazamos el valor de ${y}=\\simplify{({c}-{d2})/(2*{d}*{b})}$ en la ecuación despejada del primer paso, para obtener el valor de $x$
\n\\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}
Finalmente la solución del sistema es:
\n\\[{(x,y)}=\\left(\\simplify[std]{{d}+{b}{{({c}-{d2})/(2{d}*{b})}}},\\simplify{({c}-{d2})/(2{d}*{b})}\\right)\\]
\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", "d", "d2", "d3", "b2"], "parts": [{"variableReplacements": [], "prompt": "Ingrese su respuesta como números enteros o bien fracciones.
\n$x=$ [[0]] , $y=$ [[1]]
\n\n", "showCorrectAnswer": true, "type": "gapfill", "gaps": [{"vsetrange": [0, 1], "showCorrectAnswer": true, "marks": 1, "showFeedbackIcon": true, "checkingtype": "absdiff", "answer": "{d+(c-d^2)/(2*d)}", "notallowed": {"partialCredit": 0, "message": "Input your answer as a fraction and not a decimal.
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