Question

The math teacher asked his students to determine a solution for 1.5x−2y=8. Which solution below is the correct one?(1 point) Responses Fiona believes (4,7) is a solution. Fiona believes left parenthesis 4 comma 7 right parenthesis is a solution. Mary believes (4,−7) is a solution. Mary believes left parenthesis 4 comma negative 7 right parenthesis is a solution. Sam believes (−4,−7) is a solution. Sam believes left parenthesis negative 4 comma negative 7 right parenthesis is a solution. Peter believes (−4,7) is a solution.

Answer 1

To determine which of the points is a solution to the equation \(1.5x - 2y = 8\), we will substitute each pair of values into the equation and check if they satisfy it.

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

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

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

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

The only solution that satisfies the equation \(1.5x - 2y = 8\) is Sam's solution (-4, -7).