The equation given is $(x - y, x + y) = (6, 10)$.

This can be interpreted as two separate equations:

1. $x - y = 6$
2. $x + y = 10$

Now, let's solve for $x$ and $y$:

Step 1: Add the two equations

$(x - y) + (x + y) = 6 + 10$ $2x = 16$ $x = \frac{16}{2} = 8$

Step 2: Substitute $x = 8$ into one of the original equations

Using the first equation $x - y = 6$: $8 - y = 6$ $y = 8 - 6 = 2$

Thus, $x = 8$ and $y = 2$.

Would you like a detailed explanation or have any questions about this? Here are five related questions to explore further:

1. How would the result change if $(x + y) = 12$ instead of 10?
2. Can you solve the system of equations using substitution instead of addition?
3. What is the geometric interpretation of solving $x - y$ and $x + y$ simultaneously?
4. How would you solve for $x$ and $y$ if fractional values were involved?
5. How does solving linear systems like this apply to real-world problems?

Tip: Always check your solution by substituting values back into the original equations!