To solve the system of equations using the addition (elimination) method, we have the two equations:

1. $x + y = 6$
2. $x - y = -2$

Step 1: Add the two equations

By adding both equations together, the $y$-terms will cancel out.

$(x + y) + (x - y) = 6 + (-2)$

This simplifies to:

$2x = 4$

Step 2: Solve for $x$

Now, solve for $x$ by dividing both sides by 2:

$x = \frac{4}{2} = 2$

Step 3: Substitute $x = 2$ back into one of the original equations

Now substitute $x = 2$ into the first equation $x + y = 6$:

$2 + y = 6$

Solve for $y$:

$y = 6 - 2 = 4$

Solution

The solution to the system is:

$x = 2, \quad y = 4$

Would you like more details or have any questions?

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Here are 5 related questions:

1. Can you solve the system using the substitution method instead of the addition method?
2. What happens if we subtract the equations instead of adding them?
3. How can we represent this system of equations graphically?
4. What are some scenarios where the addition method is more efficient than substitution?
5. How can we check if the solution satisfies both original equations?

Tip: In the addition method, always ensure the coefficients of one variable cancel out to simplify the system quickly.