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.

1 answer

To determine which student found the correct solution for the equation \(3x - 4y = 8\), we need to substitute the values of \(x\) and \(y\) from each student’s solution into the equation and see if it holds true.

  1. Student #1: Linda believes \((1, -4)\) is a solution. \[ 3(1) - 4(-4) = 3 - (-16) = 3 + 16 = 19 \quad \text{(not equal to 8)} \]

  2. Student #2: Nathan believes \((5, 3)\) is a solution. \[ 3(5) - 4(3) = 15 - 12 = 3 \quad \text{(not equal to 8)} \]

  3. Student #3: Gary believes \((4, 1)\) is a solution. \[ 3(4) - 4(1) = 12 - 4 = 8 \quad \text{(equal to 8)} \]

Thus, the correct student is Student #3, Gary.

Answer: Student #3 is correct.