luhmia19 luhmia19
  • 25-04-2022
  • Mathematics
contestada

the difference between two numbers is 9. Find the numbers if their sum is 46

Respuesta :

profarouk profarouk
  • 26-04-2022

Answer:

[tex](\frac{55}{2} ,\frac{37}{2} )[/tex]

Step-by-step explanation:

We have to solve this system of equations in order to find the numbers :

Let x be greater number and y be the smaller one :

[tex]\begin{cases}x-y=9\ \ \ (1)&\\ x+y=46\ \ \ (2)&\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}y=x-9\ \ \ (1)&\\ 2x=9+46=55\ \ \ (1)+(2)&\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}y=\frac{55}{2} -9=\frac{37}{2} &\\ x=\frac{55}{2}&\end{cases}[/tex]

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