(4,−3)

Question

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 plus 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

Answer 1

To determine which system the point \((4, -3)\) is a solution for, we can substitute \(x = 4\) and \(y = -3\) into each equation in the systems provided.

Let's evaluate each option:

Option 1:

1. Equation 1: \(7x + 9y = 55\) \[ 7(4) + 9(-3) = 28 - 27 = 1 \quad (\text{not } 55) \]

2. Equation 2: \(3x - 9y = -15\) \[ 3(4) - 9(-3) = 12 + 27 = 39 \quad (\text{not } -15) \]

Option 2:

1. Equation 1: \(7x + 9y = 55\) \[ 7(4) + 9(-3) = 28 - 27 = 1 \quad (\text{not } 55) \]

2. Equation 2: \(3x + 9y = -15\) \[ 3(4) + 9(-3) = 12 - 27 = -15 \quad (\text{true}) \]

Option 3:

1. Equation 1: \(7x - 9y = 55\) \[ 7(4) - 9(-3) = 28 + 27 = 55 \quad (\text{true}) \]

2. Equation 2: \(3x - 9y = -15\) \[ 3(4) - 9(-3) = 12 + 27 = 39 \quad (\text{not } -15) \]

Option 4:

1. Equation 1: \(7x - 9y = 55\) \[ 7(4) - 9(-3) = 28 + 27 = 55 \quad (\text{true}) \]

2. Equation 2: \(3x + 9y = -15\) \[ 3(4) + 9(-3) = 12 - 27 = -15 \quad (\text{true}) \]

Conclusion:

The correct option where \((4, -3)\) is a solution to both equations is:

7x−9y=55 and 3x+9y=−15 (Option 4).