Question
Ms. Smith asked her students to determine a solution for 3x−4y=8
. Which of the following students found the correct solution?
Student #1: Linda believes (1,−4)
is a solution to the equation.
Student #2: Nathan believes (5,3)
is a solution to the equation.
Student #3: Gary believes (4,1)
is a solution to the equation.
(1 point)
. Which of the following students found the correct solution?
Student #1: Linda believes (1,−4)
is a solution to the equation.
Student #2: Nathan believes (5,3)
is a solution to the equation.
Student #3: Gary believes (4,1)
is a solution to the equation.
(1 point)
Answers
GPT-4o mini
To determine which student found the correct solution for the equation \(3x - 4y = 8\), we can substitute each student's proposed solution into the equation.
1. **Linda's solution \((1, -4)\)**:
\[
3(1) - 4(-4) = 3 - (-16) = 3 + 16 = 19 \quad \text{(not a solution)}
\]
2. **Nathan's solution \((5, 3)\)**:
\[
3(5) - 4(3) = 15 - 12 = 3 \quad \text{(not a solution)}
\]
3. **Gary's solution \((4, 1)\)**:
\[
3(4) - 4(1) = 12 - 4 = 8 \quad \text{(is a solution)}
\]
Based on these calculations, the correct solution is from **Student #3: Gary, who correctly identified \((4, 1)\)** as a solution to the equation \(3x - 4y = 8\).
1. **Linda's solution \((1, -4)\)**:
\[
3(1) - 4(-4) = 3 - (-16) = 3 + 16 = 19 \quad \text{(not a solution)}
\]
2. **Nathan's solution \((5, 3)\)**:
\[
3(5) - 4(3) = 15 - 12 = 3 \quad \text{(not a solution)}
\]
3. **Gary's solution \((4, 1)\)**:
\[
3(4) - 4(1) = 12 - 4 = 8 \quad \text{(is a solution)}
\]
Based on these calculations, the correct solution is from **Student #3: Gary, who correctly identified \((4, 1)\)** as a solution to the equation \(3x - 4y = 8\).