Andrea and Beto are siblings. Andrea is years older than Beto, and the sum of their ages is . Which of the following systems of equations could be used to find Andrea's age, , and Beto's age, ?

To find the correct system of equations to determine Andrea's age \(A\) and Beto's age \(B\), we need to translate the information provided into mathematical statements.

Given:
1. **Andrea is \(x\) years older than Beto**: This means that Andrea's age \(A\) is related to Beto's age \(B\) by the equation:
   \[
   A = B + x
   \]
2. **The sum of their ages is \(y\)**: This means that the sum of their ages is given by:
   \[
   A + B = y
   \]

Thus, the system of equations that can be used to find their ages is:

\[
\begin{cases}
A = B + x \\
A + B = y
\end{cases}
\]

### Summary of the system:
- \(A = B + x\): Andrea is \(x\) years older than Beto.
- \(A + B = y\): The sum of their ages is \(y\).

Would you like details on solving this system or have any further questions?

Here are 5 related questions for further exploration:
1. How do you solve a system of two linear equations?
2. What are the methods to solve systems of equations (substitution, elimination, etc.)?
3. Can you find a specific example of Andrea and Beto's ages for \(x = 3\) and \(y = 15\)?
4. What happens if Andrea were younger than Beto? How would the system of equations change?
5. How do systems of equations apply in real-world age problems?

**Tip**: When solving a system of equations, substitution works well when one equation is already solved for one variable, like in this problem.

Explore how to form and solve a system of linear equations based on the ages of siblings Andrea and Beto. This problem includes translating age relationships into algebraic equations. Suitable for students in Grades 6-8, this example covers key algebraic concepts such as linear equations and solving systems.

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