Question

(4,−3) 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 plus 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 plus 9 y equals 55 3 x minus 9 y equals negative 15 7x−9y=55 3x− 9y=−15

Answer 1

To determine which system has the point (4, -3) as a solution, we can substitute \(x = 4\) and \(y = -3\) into each equation in the proposed systems and see if both equations are satisfied.

Let's check each system one by one:

1. System:

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

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

   For \(3x + 9y = -15\): \[ 3(4) + 9(-3) = 12 - 27 = -15 \quad \text{(True)} \] Both equations are satisfied.

2. System:

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

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

   Since one equation is false, we can skip checking the second.

3. System:

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

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

   Since one equation is false, we can skip checking the second.

4. System:

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

   For \(7x - 9y = 55\) (this one we already checked): \[ 7(4) - 9(-3) = 55 \quad \text{(True)} \]

   For \(3x - 9y = -15\): \[ 3(4) - 9(-3) = 12 + 27 = 39 \quad \text{(False)} \]

   Since one equation is false, we can skip checking the second.

5. System:

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

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

   Since one equation is false, we can skip checking the second.

From our examination, the only system that has (4, -3) as a solution is:

7x - 9y = 55
3x + 9y = -15