(4,−3)

Question

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

7x+9y=55

3x+ 9y=−15
7 x plus 9 y is equal to 55 3x+ 9y=−15
- no response given

7x+9y=55

3x−9y=−15
7 x plus 9 y is equal to 55 3 x minus 9 y is equal to negative 15 - no response given

7x−9y=55

3x− 9y=−15
7 x minus 9 y is equal to 55 3x− 9y=−15
- incorrect

7x−9y=55

3x+ 9y=−15

Answer 1

To determine which system of equations has the solution (4, -3), we can substitute x = 4 and y = -3 into each of the given equations.

1. First System:

   • \( 7x + 9y = 55 \) \[ 7(4) + 9(-3) = 28 - 27 = 1 \quad \text{(not equal to 55)} \]
   • \( 3x + 9y = -15 \) \[ 3(4) + 9(-3) = 12 - 27 = -15 \quad \text{(correct)} \]

2. Second System:

   • \( 7x + 9y = 55 \) \[ 7(4) + 9(-3) = 28 - 27 = 1 \quad \text{(not equal to 55)} \]
   • \( 3x - 9y = -15 \) \[ 3(4) - 9(-3) = 12 + 27 = 39 \quad \text{(not equal to -15)} \]

3. Third System:

   • \( 7x - 9y = 55 \) \[ 7(4) - 9(-3) = 28 + 27 = 55 \quad \text{(correct)} \]
   • \( 3x - 9y = -15 \) \[ 3(4) - 9(-3) = 12 + 27 = 39 \quad \text{(not equal to -15)} \]

4. Fourth System:

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

Since the first and second equations from the fourth system both yield correct results when evaluated at \( (4, -3) \), the correct system for the solution \( (4, -3) \) is:

7x−9y=55 and 3x+9y=−15.