To solve the system of linear equations given:

$y = -6x - 8$ $y = -6x + 8$

we'll analyze whether there is an intersection point, meaning a solution for $(x, y)$, or if the lines are parallel.

Step 1: Compare the Slopes

Both equations have the same slope of $-6$. This indicates that the lines are parallel, as they both have the same slope but different y-intercepts. The first line has a y-intercept of $-8$, and the second line has a y-intercept of $+8$.

Step 2: Determine if There is a Solution

Since parallel lines do not intersect, there are no points $(x, y)$ that satisfy both equations simultaneously. Therefore, this system has no solution.

The solution set is empty, indicating that the system is inconsistent.

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

Here are some follow-up questions that expand on this topic:

1. How can you identify parallel lines just by looking at their equations?
2. What does it mean for a system of equations to be consistent or inconsistent?
3. How would the solution change if the y-intercepts were the same?
4. What is the difference between independent, dependent, and inconsistent systems?
5. How can we represent this system graphically?

Tip: For a system of two linear equations, if the slopes are equal and y-intercepts are different, the system is always inconsistent (no solution).