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(4,−3) is the correct solution to which system?

7x+9y=55
3x+ 9y=−15

7x−9y=55
3x− 9y=−15

7x+9y=55
3x−9y=−15

7x−9y=55
3x+ 9y=−15

1 answer

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

System 1:

  1. \(7x + 9y = 55\)

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

  2. \(3x + 9y = -15\)

    • Substitute \(x = 4\) and \(y = -3\): \[ 3(4) + 9(-3) = 12 - 27 = -15 \quad (\text{true}) \]

System 2:

  1. \(7x - 9y = 55\)

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

  2. \(3x - 9y = -15\)

    • Substitute \(x = 4\) and \(y = -3\): \[ 3(4) - 9(-3) = 12 + 27 = 39 \quad (\text{not } -15) \]

System 3:

  1. \(7x + 9y = 55\)

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

  2. \(3x - 9y = -15\)

    • Substitute \(x = 4\) and \(y = -3\): \[ 3(4) - 9(-3) = 12 + 27 = 39 \quad (\text{not } -15) \]

System 4:

  1. \(7x - 9y = 55\)

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

  2. \(3x + 9y = -15\)

    • Substitute \(x = 4\) and \(y = -3\): \[ 3(4) + 9(-3) = 12 - 27 = -15 \quad (\text{true}) \]

Conclusion:

(4, -3) is the correct solution to System 4: \[ 7x - 9y = 55 \] \[ 3x + 9y = -15 \]