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From the list of equations: 1. y=x-3 2. y=2x-6 3. 3y=3x-9 4. 3y=3x 9 Which pair of equations forms a system that has infinitely many solutions?

User Hurelu
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Final answer:

To find a system with infinitely many solutions, we compare the slopes and y-intercepts of the equations. One pair that satisfies this is y = x - 3 and 3y = 3x - 9.

Step-by-step explanation:

To determine which pair of equations forms a system with infinitely many solutions, we need to check if the slopes and y-intercepts of the equations are equal.

Let's compare the equations:

  1. y = x - 3 (slope = 1, y-intercept = -3)
  2. y = 2x - 6 (slope = 2, y-intercept = -6)
  3. 3y = 3x - 9 (slope = 1, y-intercept = -3)
  4. 3y = 3x + 9 (slope = 1, y-intercept = 3)

The pair of equations that has the same slope and y-intercept is:

  1. y = x - 3
  2. 3y = 3x - 9

Therefore, the pair of equations that forms a system with infinitely many solutions is y = x - 3 and 3y = 3x - 9.

User Laureano
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