The math teacher asked his students to determine a solution for 1.5x−2y=8

Question

. Which solution below is the correct one?(1 point)
Responses

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

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.

Answer 1

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

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

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

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

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

Thus, the correct solution to the equation \(1.5x - 2y = 8\) is given by Sam: \((-4, -7)\).