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. Sam believes (−4,−7) is a solution. Sam believes left parenthesis negative 4 comma negative 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. Peter believes (−4,7) is a solution. Peter believes left parenthesis negative 4 comma 7 right parenthesis is a solution.

Answer 1

To determine which solution is correct, we need to substitute each pair \((x, y)\) into the equation \(1.5x - 2y = 8\) and check if the equation holds true.

1. Fiona's solution: (4, 7)

   \[ 1.5(4) - 2(7) = 6 - 14 = -8 \quad \text{(not a solution)} \]

2. Sam's solution: (-4, -7)

   \[ 1.5(-4) - 2(-7) = -6 + 14 = 8 \quad \text{(this is a solution)} \]

3. Mary's solution: (4, -7)

   \[ 1.5(4) - 2(-7) = 6 + 14 = 20 \quad \text{(not a solution)} \]

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 \((-4, -7)\).