Pregunta
Set up a system. YOU DO NOT NEED TO SOLVE IT! 9. The sum of two numbers is 105 . The larger number is 6 less than twice the smaller number. What system could you use to find the two numbers?
Ask by Daniel Hobbs. in the United States
Mar 17,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
To find the two numbers, set up the following system of equations:
\[
\begin{cases}
x + y = 105 \\
y = 2x - 6
\end{cases}
\]
Solución
To set up a system of equations based on the given problem, we can define two variables:
- Let \( x \) be the smaller number.
- Let \( y \) be the larger number.
From the problem, we have the following conditions:
1. The sum of the two numbers is 105:
\[
x + y = 105
\]
2. The larger number is 6 less than twice the smaller number:
\[
y = 2x - 6
\]
Thus, the system of equations that can be used to find the two numbers is:
\[
\begin{cases}
x + y = 105 \\
y = 2x - 6
\end{cases}
\]
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Simplifique esta solución Mind Expander
Let's define the two numbers as \( x \) (the larger number) and \( y \) (the smaller number). You can set up the following system of equations: 1. \( x + y = 105 \) 2. \( x = 2y - 6 \) This system represents the relationships described in your problem and can be used to find the values of \( x \) and \( y \) when you decide to solve it!
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