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

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.

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.

Answer 1

To determine which of the given points is a solution to the equation \( 1.5x - 2y = 8 \), we need to substitute each point into the equation and check if it satisfies the equation.

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

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

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

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

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