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

Question

Sam believes (-4, -7) is a solution.
Fiona believes (4, 7) is a solution.
Peter believes (-4, 7) is a solution.
Mary believes (4,-7) is a solution.

Answer 1

To determine if any of the proposed solutions satisfy the equation \(1.5x - 2y = 8\), we can substitute each pair \((x, y)\) into the equation.

1. For Sam's solution (-4, -7): \[ 1.5(-4) - 2(-7) = -6 + 14 = 8 \] This is a valid solution.

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

3. For Peter's solution (-4, 7): \[ 1.5(-4) - 2(7) = -6 - 14 = -20 \] This is not a solution.

4. For Mary's solution (4, -7): \[ 1.5(4) - 2(-7) = 6 + 14 = 20 \] This is not a solution.

The only correct solution from the given options is Sam's \((-4, -7)\).