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Solucione las siguientes ecuaciones: \( \begin{array}{l}7.1 x+6.6 y=8.4 \\ 4.6 x-8 y=4.8 \\ \text { El valor de } x \text { es: }\end{array} \)

Ask by Perkins Lawson. in Colombia
Mar 17,2025

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El valor de \( x \) es \( \frac{2472}{2179} \).

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The Deep Dive

Para resolver el sistema de ecuaciones, podemos usar el método de sustitución o el método de eliminación. Aquí, utilizaremos el método de eliminación. Multiplicamos la primera ecuación por 4.6 y la segunda por 7.1 para alinear los coeficientes de \( x \): \[ \begin{align*} 32.66 x + 30.36 y & = 38.76 \quad \text{(Ecuación 1 multiplicada por 4.6)} \\ 32.06 x - 57.04 y & = 34.08 \quad \text{(Ecuación 2 multiplicada por 7.1)} \end{align*} \] Luego, restamos esas ecuaciones para eliminar \( x \) y resolver para \( y \). Al resolver, obtendremos los valores de \( x \) y \( y \). Al final, al calcular, el valor de \( x \) resulta ser aproximadamente 1.0.

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