The math teacher asked his students to determine a solution for 1.5x - 2y = 8. Which solution below is the correct one?
• Peter believes (-4, 7) is a solution.
• Sam believes (-4, -7) is a solution.
• Fiona believes (4, 7) is a solution.
• Mary believes (4, -7) is a solution.
To determine which solution is correct for the equation 1.5x - 2y = 8, we can substitute the values into the equation and check if it satisfies the equation.
Testing Peter's solution (-4, 7):
1.5(-4) - 2(7) = 8
-6 - 14 = 8
-20 = 8
Since -20 does not equal 8, Peter's solution is incorrect.
Testing Sam's solution (-4, -7):
1.5(-4) - 2(-7) = 8
-6 + 14 = 8
8 = 8
Since 8 equals 8, Sam's solution is correct.
Testing Fiona's solution (4, 7):
1.5(4) - 2(7) = 8
6 - 14 = 8
-8 = 8
Since -8 does not equal 8, Fiona's solution is incorrect.
Testing Mary's solution (4, -7):
1.5(4) - 2(-7) = 8
6 + 14 = 8
20 = 8
Since 20 does not equal 8, Mary's solution is incorrect.
Therefore, the correct solution is Sam's solution (-4, -7).