The math teacher asked his students to determine a solution

Question

for 1.5x - 2y = 8. Which solution
below is the correct one? (1 point)
• Mary believes (4, -7) is a solution.

Peter believes (-4, 7) is a solution.

Fiona believes (4, 7) is a
solution.

Sam believes (-4, -7) is a solution.

Answer 1

To determine which of the proposed points is a solution to the equation \( 1.5x - 2y = 8 \), we can substitute the \( x \) and \( y \) values from each point into the equation and check if the equation holds true.

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

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

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

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

The correct solution is provided by Sam: (-4, -7), as it satisfies the equation \( 1.5x - 2y = 8 \).