To solve the system by the addition method, follow these steps:

Step 1: Write down the system of equations.

$\text{1. } 2x + 2y = 6$ $\text{2. } 2x - 2y = 6$

Step 2: Add the equations to eliminate one variable.

We add the two equations together: $(2x + 2y) + (2x - 2y) = 6 + 6$ This simplifies to: $4x = 12$

Step 3: Solve for $x$.

$x = \frac{12}{4} = 3$

Step 4: Substitute $x = 3$ into one of the original equations to solve for $y$.

Substitute $x = 3$ into the first equation: $2(3) + 2y = 6$ This simplifies to: $6 + 2y = 6$ $2y = 0$ $y = 0$

Final Answer:

The solution is $(3, 0)$.

A. The solution is $(3, 0)$.

Would you like further clarification?

---

Here are 5 related questions:

1. How does the addition method differ from substitution in solving systems of equations?
2. What happens if both variables cancel out when using the addition method?
3. How can you tell if a system has no solution or infinitely many solutions?
4. What does it mean when a system of equations is inconsistent?
5. Can you solve a system with three variables using the addition method?

Tip: Always check your solution by substituting the values back into the original equations to verify.