(4,−3)

Question

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

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

7x+9y=55

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

7x−9y=55

3x+ 9y=−15

Answer 1

To determine which system of equations has (4, -3) as a solution, we can plug the values \( x = 4 \) and \( y = -3 \) into each equation of the systems provided.

1. System 1: \[ 7x - 9y = 55 \] \[ 3x - 9y = -15 \] Substitute \( x = 4 \) and \( y = -3 \):

   • For \( 7x - 9y = 55 \): \[ 7(4) - 9(-3) = 28 + 27 = 55 \quad \text{(true)} \]
   • For \( 3x - 9y = -15 \): \[ 3(4) - 9(-3) = 12 + 27 = 39 \quad \text{(false)} \]

   This system does not work.

2. System 2: \[ 7x + 9y = 55 \] \[ 3x - 9y = -15 \] Substitute \( x = 4 \) and \( y = -3 \):

   • For \( 7x + 9y = 55 \): \[ 7(4) + 9(-3) = 28 - 27 = 1 \quad \text{(false)} \]
   • For \( 3x - 9y = -15 \): \[ 3(4) - 9(-3) = 12 + 27 = 39 \quad \text{(false)} \]

   This system does not work.

3. System 3: \[ 7x + 9y = 55 \] \[ 3x + 9y = -15 \] Substitute \( x = 4 \) and \( y = -3 \):

   • For \( 7x + 9y = 55 \): \[ 7(4) + 9(-3) = 28 - 27 = 1 \quad \text{(false)} \]
   • For \( 3x + 9y = -15 \): \[ 3(4) + 9(-3) = 12 - 27 = -15 \quad \text{(true)} \]

   This system does not work.

4. System 4: \[ 7x - 9y = 55 \] \[ 3x + 9y = -15 \] Substitute \( x = 4 \) and \( y = -3 \):

   • For \( 7x - 9y = 55 \): \[ 7(4) - 9(-3) = 28 + 27 = 55 \quad \text{(true)} \]
   • For \( 3x + 9y = -15 \): \[ 3(4) + 9(-3) = 12 - 27 = -15 \quad \text{(true)} \]

   Therefore, the correct system of equations for which \( (4, -3) \) is a solution is: \[ 7x - 9y = 55 \quad \text{and} \quad 3x + 9y = -15. \]

This means the answer is System 4: \( 7x - 9y = 55 \) and \( 3x + 9y = -15 \).