To determine whether the system of equations is independent, dependent, or inconsistent, we can analyze the equations algebraically.
The first equation is:
1. y = 2x + 8
The second equation can be rewritten as:
2. y = 2x – 8
If we take a closer look, both equations have the same slope. The first equation has a slope of 2 (coming from the coefficient of x), and the second equation also has a slope of 2.
Now, let’s examine the y-intercepts. The first equation has a y-intercept of 8, while the second equation has a y-intercept of -8. Since the slopes are the same but the y-intercepts are different, this means that the two lines are parallel.
Because parallel lines never intersect, there are no solutions to this system of equations. Therefore, the system is classified as inconsistent.
In summary, since the two equations represent parallel lines with no points in common, the system is inconsistent.