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Metodo de sustitucion

Module by: Luz Correa. E-mail the author

Summary: Solucion sistema de ecuaciones lienales de 2x2 por el metodo de sustitucion

Metodo de sustitucion

MÉTODO DE SUSTITUCIÓN Este método consiste en despejar el valor de una variable cualquiera en función de la otra, en una de las ecuaciones dadas originalmente. Luego, sustituimos este valor obtenido en la ecuación original que ha quedado intacta. Veamos: EJEMPLO Solucionar el siguiente sistema de ecuaciones lineales: x + y = 3 (1) 2x + 3y = 5 (2) Solución Despejamos el valor de la variable x en la ecuación (1): x + y = 3 x = 3 - y Este valor obtenido lo sustituimos en la ecuación (2): 2x + 3y = 5 2 ( 3 - y ) + 3y = 5 Esta es una ecuación de primer grado con una sola variable, entonces, suprimiendo el paréntesis: 6 - 2y + 3y = 5 Agrupando términos semejantes: 6 + y = 5 Despejando: y = -1 Reemplazando el valor de y en la ecuación (1), obtenemos: X + y = 3 → x + ( -1) = 3 ∴ x = 4 La solución del sistema es la pareja ordenada ( 4, -1 ) que es igual a la obtenida por el método de Reducción

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