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.
To determine which student found the correct solution, we can substitute the values of the possible solutions into the equation and see which one satisfies the equation.
For option #1: (1,-4)
Substituting the values into the equation: 3(1) - 4(-4) = 3 + 16 = 19, which is not equal to 8. Therefore, this is not the correct solution.
For option #2: (5,3)
Substituting the values into the equation: 3(5) - 4(3) = 15 - 12 = 3, which is not equal to 8. Therefore, this is not the correct solution.
For option #3: (4,1)
Substituting the values into the equation: 3(4) - 4(1) = 12 - 4 = 8, which is equal to 8. Therefore, this is the correct solution.
Hence, student #3 (Gary) found the correct solution.