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
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
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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:
–