Ms. Smith asked her students to determine a solution for 3x−4y=8

Question

. 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.

Answer 1

To determine which of the students found the correct solution for the equation \(3x - 4y = 8\), we can substitute the proposed solutions into the equation and check if they satisfy it.

1. For Linda's solution (1, -4): \[ 3(1) - 4(-4) = 3 - (-16) = 3 + 16 = 19 \neq 8 \] So, Linda did not find the correct solution.

2. For Nathan's solution (5, 3): \[ 3(5) - 4(3) = 15 - 12 = 3 \neq 8 \] So, Nathan did not find the correct solution.

3. For Gary's solution (4, 1): \[ 3(4) - 4(1) = 12 - 4 = 8 \] So, Gary found the correct solution.

Conclusion: Student #3, Gary, found the correct solution to the equation \(3x - 4y = 8\).