Drag each pair of equations to show if the system has no solutions, one solution, or infinitely many solutions y = 3x + 4 2y = -6x + 8 y = -x – 2 y = -x – 6 y = 9x – 1 y = x + 9 y = 2x y = -2x y = -3 x = -6

Let’s analyze each pair of equations to determine their solution sets.

1. y = 3x + 4 and 2y = -6x + 8:

– Rewrite the second equation: ( y = -3x + 4 ).

– These two lines are not parallel (they have different slopes) and will intersect at one point.

– One solution.

2. y = -x – 2 and y = -x – 6:

– Both equations have the same slope (-1) but different y-intercepts (-2 and -6).

– Since they are parallel, they will never intersect.

– No solutions.

3. y = 9x – 1 and y = x + 9:

– Rewrite the second equation as ( y – x = 9 ) or ( y = x + 9 ).

– Here, the two lines have different slopes (9 and 1), so they will intersect at one point.

– One solution.

4. y = 2x and y = -2x:

– These equations describe lines with slopes of 2 and -2, respectively. They are not parallel and will intersect at one point.

– One solution.

5. y = -3 and x = -6:

–