The problem asks to represent two numbers using variables $x$ and $y$. The conditions provided are:

1. The sum of the two numbers is 2.
2. The difference of the two numbers (when one is subtracted from the other) is 6.

Based on this, we can set up the following system of equations:

• $x + y = 2$ (the sum of the numbers is 2)
• $x - y = 6$ (the difference of the numbers is 6)

Now let's check the given options in the image:

• Option A shows: x + y &= 2 \\ x - y &= 6 \end{aligned}$$ This matches the system of equations we derived from the problem description.
• Other options (B, C, D) show equations that do not match the conditions provided in the problem.

Thus, the correct answer is Option A.

Would you like me to solve the system of equations for the values of $x$ and $y$?

Here are 5 related questions to expand your understanding:

1. How do you solve a system of equations using substitution?
2. What is the graphical interpretation of solving a system of equations?
3. How would the system change if the sum was a different value?
4. What if both numbers are negative, would this system still hold?
5. What method can be used to solve a system of equations with three variables?

Tip: When solving a system of linear equations, you can use substitution, elimination, or graphical methods depending on which is most efficient for the given situation.