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)

Question

Student # is correct.

Answer 1

To determine which student found the correct solution to the equation \( 3x - 4y = 8 \), we can substitute each student's proposed solution into the equation.

1. For Linda's solution (1, -4): \[ 3(1) - 4(-4) = 3 - (-16) = 3 + 16 = 19 \quad (\text{not } 8) \] So, Linda's solution is incorrect.

2. For Nathan's solution (5, 3): \[ 3(5) - 4(3) = 15 - 12 = 3 \quad (\text{not } 8) \] So, Nathan's solution is incorrect.

3. For Gary's solution (4, 1): \[ 3(4) - 4(1) = 12 - 4 = 8 \quad (\text{this is correct}) \]

Based on this, the student who found the correct solution is:

Student #3: Gary is correct.