The math teacher asked his students to determine a solution for 1.5x − 2y = 8. Which solution below is the correct one?

Question

A) Mary believes (4, −7) is a solution.
B) Fiona believes (4, 7) is a solution.
C) Sam believes (−4, −7) is a solution.
D) Peter believes (−4,7) is a solution.

Answer 1

To determine which student has the correct solution for the equation \(1.5x - 2y = 8\), we will plug each proposed solution into the equation and check if it holds true.

1. Mary's solution (4, -7): \[ 1.5(4) - 2(-7) = 6 + 14 = 20 \quad (\text{not } 8) \] This is not a solution.

2. Fiona's solution (4, 7): \[ 1.5(4) - 2(7) = 6 - 14 = -8 \quad (\text{not } 8) \] This is not a solution.

3. Sam's solution (-4, -7): \[ 1.5(-4) - 2(-7) = -6 + 14 = 8 \quad (\text{is } 8) \] This is a solution.

4. Peter's solution (-4, 7): \[ 1.5(-4) - 2(7) = -6 - 14 = -20 \quad (\text{not } 8) \] This is not a solution.

The only correct solution is Sam's: (−4, −7).