The math teacher asked his students to determine a solution for
1.5x - 2y = 8. Which solution below is the correct one? (1 point)
• Mary believes (4, -7) is a solution.
• Fiona believes (4, 7) is a solution.
• Sam believes (—4, —7) is a solution.
• Peter believes (—4, 7) is a solution.
To determine which solution is correct, we can substitute each solution into the equation and see if it satisfies the equation.
1. Mary believes (4, -7) is a solution.
Substituting x=4 and y=-7 into the equation:
1.5(4) - 2(-7) = 6 + 14 = 20
The equation does not hold, so (4, -7) is not a solution.
2. Fiona believes (4, 7) is a solution.
Substituting x=4 and y=7 into the equation:
1.5(4) - 2(7) = 6 - 14 = -8
The equation does not hold, so (4, 7) is not a solution.
3. Sam believes (-4, -7) is a solution.
Substituting x=-4 and y=-7 into the equation:
1.5(-4) - 2(-7) = -6 + 14 = 8
The equation holds, so (-4, -7) is a solution.
4. Peter believes (-4, 7) is a solution.
Substituting x=-4 and y=7 into the equation:
1.5(-4) - 2(7) = -6 - 14 = -20
The equation does not hold, so (-4, 7) is not a solution.
Based on the calculations, the correct solution is (-4, -7), which was Sam's solution.
To determine if a given pair of values is a solution for the equation 1.5x - 2y = 8, we need to substitute the values into the equation and check if it holds true.
Let's check each option:
1. Mary believes (4, -7) is a solution.
Substitute x = 4 and y = -7 into the equation:
1.5(4) - 2(-7) = 8
6 + 14 = 8
20 ≠ 8
2. Fiona believes (4, 7) is a solution.
Substitute x = 4 and y = 7 into the equation:
1.5(4) - 2(7) = 8
6 - 14 = 8
-8 ≠ 8
3. Sam believes (-4, -7) is a solution.
Substitute x = -4 and y = -7 into the equation:
1.5(-4) - 2(-7) = 8
-6 + 14 = 8
8 = 8
4. Peter believes (-4, 7) is a solution.
Substitute x = -4 and y = 7 into the equation:
1.5(-4) - 2(7) = 8
-6 - 14 = 8
-20 ≠ 8
From the given options, only Sam's belief that (-4, -7) is a solution is correct.
To determine which solution is correct for the equation 1.5x - 2y = 8, we need to substitute the values of x and y into the equation and see if it holds true.
Let's check each solution:
1. Mary believes (4, -7) is a solution.
Plugging in x = 4 and y = -7 into the equation:
1.5(4) - 2(-7) = 8
6 + 14 ≠ 8
So, (4, -7) is not a solution.
2. Fiona believes (4, 7) is a solution.
Plugging in x = 4 and y = 7 into the equation:
1.5(4) - 2(7) = 8
6 - 14 ≠ 8
So, (4, 7) is not a solution.
3. Sam believes (-4, -7) is a solution.
Plugging in x = -4 and y = -7 into the equation:
1.5(-4) - 2(-7) = 8
-6 + 14 ≠ 8
So, (-4, -7) is not a solution.
4. Peter believes (-4, 7) is a solution.
Plugging in x = -4 and y = 7 into the equation:
1.5(-4) - 2(7) = 8
-6 - 14 = 8
-20 ≠ 8
So, (-4, 7) is also not a solution.
Considering the above calculations, none of the given solutions (4, -7), (4, 7), (-4, -7), or (-4, 7) satisfy the equation 1.5x - 2y = 8.