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:

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.