// Numbas version: exam_results_page_options {"name": "Sistema de Ecuaciones (2x2) (1)", "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 Lineales:

\\[\\begin{eqnarray*} \\simplify{{a}x+{b}y}&=&\\var{c}\\\\\\simplify{{a1}x+{b1}y}&=&\\var{c1}\\end{eqnarray*}\\]

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

Resolvamos el sistema por el método de Reducción.

Multiplique 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 $y$:

\\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:

\\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} \\]

Así:

\\[x = \\simplify[std]{{(c*b1-c1*b)/(a*b1-a1*b)}}\\]

Sustituya este valor de $x=\\simplify[std]{{(c*b1-c1*b)/(a*b1-a1*b)}}$ en la primera ecuación y resuelva para obtener $y$:

\\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}

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Shows how to define variables to stop degenerate examples.

"}, "ungrouped_variables": ["a", "c", "b", "a1", "b1", "c1"], "parts": [{"variableReplacements": [], "prompt": "

$x=$ [[0]]

$y=$ [[1]]

Ingrese su respuesta como números enteros o bien fracciones.

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Input your answer as a fraction and not a decimal.

Input your answer as a fraction and not as a decimal.

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