To solve the system of equations:

1. **Equation 1:** \( x + y = 5 \)
2. **Equation 2:** \( x - y = 7 \)

### Step 1: Add the two equations
\[
(x + y) + (x - y) = 5 + 7
\]
This simplifies to:
\[
2x = 12
\]
So, \( x = \frac{12}{2} = 6 \).

### Step 2: Substitute \( x = 6 \) into one of the original equations
Using Equation 1:
\[
6 + y = 5
\]
Solving for \( y \):
\[
y = 5 - 6 = -1
\]

### Final Solution:
\[
x = 6, \quad y = -1
\]

Would you like more details on this process or have any questions?

Here are 5 related questions to expand your understanding:

1. What happens if you subtract the two original equations instead of adding them?
2. How can you check if the solution \( x = 6 \) and \( y = -1 \) satisfies both original equations?
3. How would you solve these equations using substitution instead of elimination?
4. What would the solution be if the equations were \( x + y = 5 \) and \( x - y = -7 \)?
5. Can this method be applied to non-linear equations as well? Why or why not?

**Tip:** Always verify your solution by plugging the values back into the original equations.

Learn how to solve a system of linear equations x + y = 5 and x - y = 7 step-by-step. This problem involves using the elimination method and substitution method to find the values of x and y. Suitable for students in Grades 9-12.

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