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!

Learn how to solve the system of equations where (x - y, x + y) = (6, 10). This step-by-step guide covers solving for x and y using algebraic techniques like addition and substitution, suitable for students in Grades 7-9.

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