I need to determine if they are open, infinite, or none.

y = -1/4x + 1
8y = -2x + 8
Open
Infinite
None*

y = 6x + 2
3y = 18x + 12
Open
Infinite*
None

-2y = -x + 6
y = 1/2x - 3
Open
Infinite
None*

y = 5x - 6
3y = 15x - 12
Open
Infinite
None*

y = -1/4x + 1

8y = -2x + 8
Open
Infinite
None* YES PARALLEL

y = 6x + 2
3y = 18x + 12
Open
Infinite*
None SAME SLOPE BUT DIFFERENT Y AXIS INTERCEPTS, NEVER CROSS

-2y = -x + 6
y = 1/2x - 3
Open
Infinite SAME SLOPE SAME INTERCEPT, THE SAME EVERYWHERE INFINITE
None*

y = 5x - 6
3y = 15x - 12
Open
Infinite
None* YES, SAME SLOPE, DIFFERENT INTERCEPTS, NEVER CROSS

SORRY, FIRST ONE IS INFINITE, SAME SLOPE, SAME INTERCEPT

To determine if a system of equations has an open, infinite, or no solution, you can analyze the coefficients of the variables and the constants in the equations. Here is the step-by-step process to determine the solution type for each system of equations you provided:

1. y = -1/4x + 1
8y = -2x + 8

To analyze the coefficients of x and y, compare the slopes (coefficients of x) in both equations. Since they have different slopes (-1/4 and -2), the lines will intersect at a single point, which means they have an open solution.

2. y = 6x + 2
3y = 18x + 12

Again, compare the slopes (coefficients of x) in both equations. Here, both equations have the same slope of 6, which means the lines are parallel. Parallel lines never intersect, so the system has no solution.

3. -2y = -x + 6
y = 1/2x - 3

Compare the slopes (coefficients of x) in both equations. They are different, -1/2 and 1/2, respectively. This means they will intersect at a single point, so the system has an open solution.

4. y = 5x - 6
3y = 15x - 12

Once again, compare the slopes (coefficients of x) in both equations. They are the same, 5 and 15. This implies that the lines are coincident or overlapping, meaning they have an infinite number of solutions.

So, the solutions for each system are as follows:
1. Open
2. None
3. Open
4. Infinite