Carmen y Catalina comparan la nota que obtuvieron en su examen bimestral de Aritmética y mencionan lo siguiente: Nuestras notas juntas es igual a 34 puntos, pero se sabe que Carmen obtuvo 4 puntos más que Catalina. ¿Cuál es la nota de Catalina?

Answer:

La nota de Carolina es 15 puntos.

Step-by-step explanation:

Un sistema de ecuaciones lineales es un conjunto de ecuaciones lineales que tienen más de una incógnita, relacionadas mediante las ecuaciones.

En los sistemas de ecuaciones, se debe buscar los valores de las incógnitas.  Al reemplazar en las ecuaciones, deben dar la solución planteada.

En este caso se debe plantear un sistema de ecuaciones, donde las incógnitas son:

Ambas notas juntas es igual a 34 puntos. Expresado matemáticamente es:

x + y= 34

Se sabe que Carmen obtuvo 4 puntos más que Catalina. Esto es:

y= x + 4

Entonces el sistema de ecuaciones a resolver es:

[tex]\left \{ {{x+y=34} \atop {y=x+4}} \right.[/tex]

A través del método de sustitución debes despejar una de las incógnitas en una de las ecuaciones y sustituir su valor en la siguiente. En este caso, ya tienes despejada la incógnita y en la segunda ecuación. Por lo que sustituyes esta expresión en la primer ecuación:

x+ x+4=34

Resolviendo obtienes:

x + x= 34 - 4

2*x=30

x= 30÷ 2

x=15

Sustituyendo este valor en la segunda ecuación obtienes:

y= x+4

y= 15 +4

y= 19

Recordando que "x" representa la nota de Carolina e "y" la nota de Carmen, entonces la nota de Carolina es 15 puntos y la nota de Carmen es 19 puntos.

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