To solve the given system of equations using the elimination method:

System of Equations:

1. $y = 2x + 8$
2. $y = -2x$

Step 1: Set the equations equal to each other

Since both equations equal $y$, set them equal: $2x + 8 = -2x$

Step 2: Eliminate $x$ by simplifying

Add $2x$ to both sides to eliminate the negative term: $2x + 2x + 8 = 0$ $4x + 8 = 0$

Step 3: Solve for $x$

Subtract 8 from both sides: $4x = -8$ Divide by 4: $x = -2$

Step 4: Substitute $x = -2$ into one of the original equations

Using the second equation ($y = -2x$): $y = -2(-2)$ $y = 4$

Final Solution:

$x = -2, \, y = 4$

Would you like a detailed explanation of why elimination works, or do you have other questions?

Related Questions:

1. How does substitution compare to elimination for solving systems of equations?
2. Can we use graphing to verify this solution?
3. How do you solve systems with three variables using elimination?
4. What happens if the system has no solution or infinitely many solutions?
5. Can elimination work with non-linear systems of equations?

Tip: Always check your solution by substituting the values of $x$ and $y$ back into both original equations!