To solve this system of linear equations:

$y = -2x - 4$ $y = 2x - 4$

we can set the two equations equal to each other since both are equal to $y$:

$-2x - 4 = 2x - 4$

Now, we can solve for $x$.

1. Add $2x$ to both sides: $-4 = 4x - 4$

2. Add $4$ to both sides: $0 = 4x$

3. Divide by 4: $x = 0$

Now that we have $x = 0$, we can substitute it back into either equation to find $y$. Let's use the first equation:

$y = -2(0) - 4 = -4$

Thus, the solution to the system is: $(x, y) = (0, -4)$

Would you like further explanation on any part of this solution?

Here are 5 additional questions to deepen your understanding:

1. How would you graphically interpret the solution of this system?
2. What happens if two equations in a system are parallel?
3. How would you solve the system if both equations had the same slope and intercept?
4. Can you solve a similar system using substitution for different equations?
5. How would you verify the solution by plugging values back into the original equations?

Tip: For systems of equations, always check if substitution or elimination is more efficient based on the form of the equations.