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

Answer 1

To determine which of the given pairs is a solution for the equation \(1.5x - 2y = 8\), we can substitute each pair into the equation and see if it holds true.

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

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

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

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

After evaluating all the provided solutions, the only correct solution for the equation \(1.5x - 2y = 8\) is Sam's solution \((-4, -7)\).