Question
The math teacher asked his students to determine a solution for 1.5x - 2y = 8. Which solution below is the correct one?
Sam believes (-4, -7) is a solution.
Fiona believes (4, 7) is a solution.
Peter believes (-4, 7) is a solution.
Mary believes (4,-7) is a solution.
Sam believes (-4, -7) is a solution.
Fiona believes (4, 7) is a solution.
Peter believes (-4, 7) is a solution.
Mary believes (4,-7) is a solution.
Answers
GPT-4o mini
To determine if any of the proposed solutions satisfy the equation \(1.5x - 2y = 8\), we can substitute each pair \((x, y)\) into the equation.
1. **For Sam's solution (-4, -7)**:
\[
1.5(-4) - 2(-7) = -6 + 14 = 8
\]
This is a valid solution.
2. **For Fiona's solution (4, 7)**:
\[
1.5(4) - 2(7) = 6 - 14 = -8
\]
This is not a solution.
3. **For Peter's solution (-4, 7)**:
\[
1.5(-4) - 2(7) = -6 - 14 = -20
\]
This is not a solution.
4. **For Mary's solution (4, -7)**:
\[
1.5(4) - 2(-7) = 6 + 14 = 20
\]
This is not a solution.
The only correct solution from the given options is Sam's \((-4, -7)\).
1. **For Sam's solution (-4, -7)**:
\[
1.5(-4) - 2(-7) = -6 + 14 = 8
\]
This is a valid solution.
2. **For Fiona's solution (4, 7)**:
\[
1.5(4) - 2(7) = 6 - 14 = -8
\]
This is not a solution.
3. **For Peter's solution (-4, 7)**:
\[
1.5(-4) - 2(7) = -6 - 14 = -20
\]
This is not a solution.
4. **For Mary's solution (4, -7)**:
\[
1.5(4) - 2(-7) = 6 + 14 = 20
\]
This is not a solution.
The only correct solution from the given options is Sam's \((-4, -7)\).