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Zepler [3.9K]
3 years ago
8

X+5y=5 3x-5y=3 Necesito ayuda, procedimiento para resolverlos y maneras distintas de resolverlos. Denuncio a quien venga por los

puntos.
Mathematics
1 answer:
qaws [65]3 years ago
5 0

Answer:

Se puede resolver el sistema de ecuaciones por sustitución, igualación o determinante. La solución de este sistema es (x,y) = \left(2,\frac{3}{5} \right).

Step-by-step explanation:

Sea el sistema de ecuaciones que se describe abajo:

x+5\cdot y = 5 (1)

3\cdot x -5\cdot y = 3 (2)

Existen por lo menos tres métodos analíticos para la resolución de este sistema de ecuaciones:

(i) Sustitución

Despejamos x en (1):

x = 5-5\cdot y

Aplicamos la expresión resultante en (2):

3\cdot \left(5-5\cdot y\right)-5\cdot y = 3

Luego, resolvemos la ecuación resultante:

15  - 15\cdot y -5\cdot y = 3

-20\cdot y = -12

y = \frac{3}{5}

Luego, determinamos el valor de x:

x = 2

(ii) Igualación

Despejamos 5\cdot y en cada expresión:

5\cdot y = 5 - x (3)

5\cdot y = 3\cdot x - 3 (4)

Ahora, igualamos (3) y (4) y simplificamos:

5-x = 3\cdot x -3

4\cdot x = 8

x = 2

Finalmente, calculamos y en (3):

y = 1 - \frac{x}{5}

y = \frac{3}{5}

(iii) Determinante

Aplicamos las siguientes fórmulas para determinar cada variable:

x = \frac{\left|\begin{array}{ccc}5&5\\3&-5\end{array}\right| }{\left|\begin{array}{ccc}1&5\\3&-5\end{array}\right|}

x = \frac{-25-15}{-5-15}

x = 2

y = \frac{\left|\begin{array}{ccc}1&5\\3&3\end{array}\right| }{\left|\begin{array}{ccc}1&5\\3&-5\end{array}\right|}

y = \frac{3-15}{-5-15}

y = \frac{3}{5}

Por ende, concluimos que la solución de este sistema es (x,y) = \left(2,\frac{3}{5} \right).

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