https://file.aiquickdraw.com/mathbot/file/17268604663981zzk7pv5.jpg

Let's solve the given system of equations step by step:

The system of equations is:

\[
\begin{aligned}
1) \quad x + y &= 8 \\
2) \quad x - y &= 4
\end{aligned}
\]

### Step 1: Add the two equations
When we add equation 1 and equation 2, the \(y\)-terms will cancel out:

\[
(x + y) + (x - y) = 8 + 4
\]

This simplifies to:

\[
2x = 12
\]

Solving for \(x\):

\[
x = \frac{12}{2} = 6
\]

### Step 2: Substitute \(x = 6\) into one of the original equations
Now, substitute \(x = 6\) into equation 1:

\[
6 + y = 8
\]

Solving for \(y\):

\[
y = 8 - 6 = 2
\]

### Step 3: Verify the solution
Let's substitute \(x = 6\) and \(y = 2\) into the second equation to verify:

\[
6 - 2 = 4
\]

Both equations are satisfied, so the solution is correct.

### Final Answer:
The solution is \(x = 6\) and \(y = 2\).

In the given options:

- **Option A** is correct: The solution is \(x = 6\) and \(y = 2\).
  
Let me know if you would like more details or further clarification! Here are some related questions for additional practice:

1. What is the graphical interpretation of solving a system of linear equations?
2. How would the solution change if the system had no solutions (i.e., was inconsistent)?
3. Can two linear equations have infinitely many solutions? If so, under what conditions?
4. How do you solve a system of equations by substitution instead of addition?
5. What are the possible outcomes (number of solutions) when solving a system of linear equations?

**Tip:** For a system of linear equations, if the lines are parallel, the system is inconsistent, meaning there is no solution.

Solve the system of equations. If the system has no solution, say that it is inconsistent. Graph the lines of the system: x + y = 8 and x - y = 4.

Learn how to solve the system of linear equations x + y = 8 and x - y = 4 by addition, substitution, and verification. This problem explores key algebraic concepts in solving a system of equations. Suitable for Grades 8-10.

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