Final answer:
The system of equations y = -6x - 8 and y = -6x + 8 have no solution as they represent parallel lines with different y-intercepts; therefore, they never intersect.
Step-by-step explanation:
To solve the system of equations y = -6x - 8 and y = -6x + 8, we set the two equations equal to each other since they both define y in terms of x. However, when we do this, we get -6x - 8 = -6x + 8.
This results in a contradiction because the two sides of the equation can never be equal (subtracting 8 from something cannot give you the same result as adding 8 to it). This indicates that there is no point (x, y) that satisfies both equations at the same time.
The two lines represented by the equations are parallel since they have identical slopes but different y-intercepts. Therefore, the solution to this system of equations is that there is no intersection and hence no solution.