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) Student # is correct

Answer 1

To determine which student found a correct solution to the equation \(3x - 4y = 8\), we will substitute the candidates' points into the equation.

1. Student #1: Linda believes (1,−4): \[ x = 1, \quad y = -4 \] Substitute into the equation: \[ 3(1) - 4(-4) = 3 + 16 = 19 \quad (\text{not } 8) \]

2. Student #2: Nathan believes (5,3): \[ x = 5, \quad y = 3 \] Substitute into the equation: \[ 3(5) - 4(3) = 15 - 12 = 3 \quad (\text{not } 8) \]

3. Student #3: Gary believes (4,1): \[ x = 4, \quad y = 1 \] Substitute into the equation: \[ 3(4) - 4(1) = 12 - 4 = 8 \quad (\text{is } 8) \]

The correct solution is found by Student #3: Gary. So, the answer is Student #3 is correct.