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Let's solve the system of equations using the addition method (also known as the elimination method). The system of equations is:

\[
\begin{aligned}
3x + 8y &= 3 \\
4x - 8y &= 4
\end{aligned}
\]

### Step 1: Add the two equations together.

Since the coefficients of \( y \) are opposites (\( 8y \) and \( -8y \)), adding the two equations will eliminate \( y \).

\[
(3x + 8y) + (4x - 8y) = 3 + 4
\]

Simplifying:

\[
3x + 4x + 8y - 8y = 7
\]

\[
7x = 7
\]

### Step 2: Solve for \( x \).

\[
x = \frac{7}{7} = 1
\]

### Step 3: Substitute \( x = 1 \) back into one of the original equations to solve for \( y \).

Let's use the first equation:

\[
3(1) + 8y = 3
\]

Simplifying:

\[
3 + 8y = 3
\]

\[
8y = 3 - 3
\]

\[
8y = 0
\]

\[
y = \frac{0}{8} = 0
\]

### Final Solution:

The solution to the system is \( x = 1 \) and \( y = 0 \), or as an ordered pair, \( (1, 0) \).

### Answer:

The correct choice is **A. The solution set is \((1, 0)\)**.

Would you like further details on any of the steps? 

Here are 5 related questions you might find useful:
1. What is the elimination (addition) method and when is it used?
2. How can we solve the system using the substitution method instead?
3. What happens if there are no opposites to eliminate a variable in a system?
4. Can you explain how systems with no solution or infinitely many solutions look like graphically?
5. How can we check if our solution is correct by substitution?

**Tip:** Always check your solution by substituting both \( x \) and \( y \) back into the original equations.

Solve the system by the addition method: 3x + 8y = 3 and 4x - 8y = 4.

This problem involves solving a system of linear equations using the addition method. By adding the equations 3x + 8y = 3 and 4x - 8y = 4, we eliminate y, solve for x, and substitute back to find y. Suitable for students in Grades 9-10.

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