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(4,−3)

is the correct solution to which system?(1 point)
Responses

7x+9y=55

3x−9y=−15
7 x plus 9 y equals 55 3 x minus 9 y equals negative 15

7x−9y=55

3x+ 9y=−15
7 x minus 9 y equals 55 3 x plus 9 y equals negative 15

7x−9y=55

3x− 9y=−15
7 x minus 9 y equals 55 3 x minus 9 y equals negative 15

7x+9y=55

3x+ 9y=−15

1 answer

To determine which system has the correct solution (4, -3), we can substitute x = 4 and y = -3 into each system of equations and check if both equations hold true.

Let's evaluate each system one by one:

1. System:

  • \( 7x + 9y = 55 \)
  • \( 3x - 9y = -15 \)

Substituting \( x = 4 \) and \( y = -3 \):

  • For \( 7x + 9y \): \[ 7(4) + 9(-3) = 28 - 27 = 1 \neq 55 \] (Does not hold)

  • For \( 3x - 9y \): \[ 3(4) - 9(-3) = 12 + 27 = 39 \neq -15 \] (Does not hold)

2. System:

  • \( 7x - 9y = 55 \)
  • \( 3x + 9y = -15 \)

Substituting \( x = 4 \) and \( y = -3 \):

  • For \( 7x - 9y \): \[ 7(4) - 9(-3) = 28 + 27 = 55 \] (Holds)

  • For \( 3x + 9y \): \[ 3(4) + 9(-3) = 12 - 27 = -15 \] (Holds)

3. System:

  • \( 7x - 9y = 55 \)
  • \( 3x - 9y = -15 \)

Substituting \( x = 4 \) and \( y = -3 \):

  • For \( 7x - 9y \): \[ 7(4) - 9(-3) = 28 + 27 = 55 \] (Holds)

  • For \( 3x - 9y \): \[ 3(4) - 9(-3) = 12 + 27 = 39 \neq -15 \] (Does not hold)

4. System:

  • \( 7x + 9y = 55 \)
  • \( 3x + 9y = -15 \)

Substituting \( x = 4 \) and \( y = -3 \):

  • For \( 7x + 9y \): \[ 7(4) + 9(-3) = 28 - 27 = 1 \neq 55 \] (Does not hold)

  • For \( 3x + 9y \): \[ 3(4) + 9(-3) = 12 - 27 = -15 \] (Holds)

Based on this evaluation, the correct system is the second system:

  • \( 7x - 9y = 55 \)
  • \( 3x + 9y = -15 \)