Respuesta :

Answer:

  • Option D

Step-by-step explanation:

Let's verify all the options.

Option A:

  • => 3y = -5x + 7

             3x = -5y - 7

  • => 3y = -5x + 7

             5y = -3x - 7

  • => 3(3y) = 3(-5x + 7)

             5(5y) = 5(-3x - 7)

  • => 9y = -15x + 21

            25y = -15x - 35

  • => 34y = -14
  • => y = -14/34
  • => y = -7/17

Hence, this is not possible for infinitely many solution.

Option B:

  • => 3y = x - 4

            -12 = 3x - 9y

  • => 3y = x - 4

             9y = 3x + 12

  • => 3(3y) = 3(x - 4)

              9y = 3x + 12

  • => 9y = 3x - 12

             9y = 3x + 12

  • => 0 = -24

Hence, this is not possible for infinitely many solution.

Option C:

  • => 2x + y = 2

           -4x - 2y = 4

  • => 2(2x + y) = 2(2)

            -4x - 2y = 4

  • => 4x + 2y = 4

             -4x - 2y = 4

  • => 0 ≠ 8

Hence, this is not possible for infinitely many solution.

Option D:

  • => 2y = 3x + 6

            4y = 6x + 12

  • => 2(2y) = 2(3x + 6)

             4y = 6x + 12

  • => 4y = 6x + 12

             4y = 6x + 12

  • => 0 = 0

Hence, this is the system that has infinitely many solutions.

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Hoped this helped.

[tex]BrainiacUser1357[/tex]

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