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To solve this system of linear equations using the addition method, we need to analyze the two given equations:

1. \( 4x + 16y = 4 \)
2. \( 4x - 16y = 4 \)

### Step-by-Step Solution:

1. **Align the equations:**
   \[
   \begin{aligned}
   4x + 16y &= 4 \\
   4x - 16y &= 4
   \end{aligned}
   \]
   
2. **Add the two equations:**
   Adding them will eliminate the \(y\)-terms:
   \[
   (4x + 16y) + (4x - 16y) = 4 + 4
   \]
   This simplifies to:
   \[
   8x = 8
   \]
   
3. **Solve for \(x\):**
   \[
   x = \frac{8}{8} = 1
   \]
   
4. **Substitute \(x = 1\) into one of the original equations:**
   Let's use the first equation:
   \[
   4(1) + 16y = 4
   \]
   Simplifying:
   \[
   4 + 16y = 4
   \]
   Subtract 4 from both sides:
   \[
   16y = 0
   \]
   Solve for \(y\):
   \[
   y = \frac{0}{16} = 0
   \]

### Conclusion:
The solution is \( x = 1 \) and \( y = 0 \), so the ordered pair is \( (1, 0) \).

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

---

Would you like more details, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. How would you solve a system of equations if the coefficients of both variables were different?
2. What would happen if the two equations had no solutions?
3. How can you verify if a system of equations has infinitely many solutions?
4. What other methods besides addition can be used to solve systems of equations?
5. Can you use substitution for this system? If yes, how?

**Tip:** When solving systems of equations, always check if adding or subtracting the equations directly simplifies your work.

Solve the system of equations using the addition method: 4x + 16y = 4 and 4x - 16y = 4.

Learn how to solve the system of equations 4x + 16y = 4 and 4x - 16y = 4 using the addition method. Follow a step-by-step solution to eliminate variables and find the ordered pair solution (1, 0). Suitable for Grades 9-10 students.

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