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, -1) 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 solutions is correct for the equation \(1.5x - 2y = 8\), we will substitute each pair of values \((x, y)\) into the equation.

1. Mary: (4, -1) \[ 1.5(4) - 2(-1) = 6 + 2 = 8 \quad \text{(this is a solution)} \]

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

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

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

The pairs (4, -1) (Mary) and (-4, -7) (Sam) are valid solutions for the equation \(1.5x - 2y = 8\).

Hence, both Mary and Sam provided correct solutions. However, since the question specifically asks for "the correct one" and only one can be chosen, Mary's solution, (4, -1), is a solution.