Question

Which system of equations has infinitely many solutions?
please help!!!

Answer 1

• Option D

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.

`BrainiacUser1357`