Equations in Two Variables Quick Check

Question

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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

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.

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.
Peter believes left parenthesis negative 4 comma 7 right parenthesis is a solution.
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Answer 1

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

1. For Sam's solution \((-4, -7)\): \[ 1.5(-4) - 2(-7) = -6 + 14 = 8 \] This is a solution.

2. For Mary's solution \((4, -7)\): \[ 1.5(4) - 2(-7) = 6 + 14 = 20 \] This is not a solution.

3. For Fiona's solution \((4, 7)\): \[ 1.5(4) - 2(7) = 6 - 14 = -8 \] This is not a solution.

4. For Peter's solution \((-4, 7)\): \[ 1.5(-4) - 2(7) = -6 - 14 = -20 \] This is not a solution.

So, the only correct solution to the equation \(1.5x - 2y = 8\) is Sam's belief that \((-4, -7)\) is a solution.