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.
To determine if a point is a solution to the equation, we need to substitute the values into the equation and check if it holds true.
For Student #1:
Substituting x = 1 and y = -4 into the equation:
3(1) - 4(-4) = 3 + 16 = 19
So, (1, -4) is not a solution to the equation.
For Student #2:
Substituting x = 5 and y = 3 into the equation:
3(5) - 4(3) = 15 - 12 = 3
So, (5, 3) is not a solution to the equation.
For Student #3:
Substituting x = 4 and y = 1 into the equation:
3(4) - 4(1) = 12 - 4 = 8
So, (4, 1) is a solution to the equation.
Therefore, the correct solution was found by Student #3.
To determine which student found the correct solution for the equation 3x - 4y = 8, we can substitute the values provided by each student into the equation and check if the equation holds true.
Let's substitute the values provided by each student into the equation:
Student #1: Linda believes (1, -4) is a solution.
Substituting these values into the equation:
3(1) - 4(-4) = 3 + 16 = 19, which is not equal to 8.
Student #2: Nathan believes (5, 3) is a solution.
Substituting these values into the equation:
3(5) - 4(3) = 15 - 12 = 3, which is not equal to 8.
Student #3: Gary believes (4, 1) is a solution.
Substituting these values into the equation:
3(4) - 4(1) = 12 - 4 = 8, which is equal to 8.
Therefore, Student #3, Gary, found the correct solution to the equation.
To determine which student found the correct solution, we need to test each of the given solutions in the equation and see if they satisfy it.
For the equation 3x - 4y = 8, we can substitute the x and y values from each of the solutions provided and check if the equation holds true.
1. Let's test Student #1's solution:
Substituting x = 1 and y = -4 into the equation:
3(1) - 4(-4) = 8
3 + 16 = 8
19 ≠ 8
2. Next, let's test Student #2's solution:
Substituting x = 5 and y = 3 into the equation:
3(5) - 4(3) = 8
15 - 12 = 8
3 ≠ 8
3. Now, let's test Student #3's solution:
Substituting x = 4 and y = 1 into the equation:
3(4) - 4(1) = 8
12 - 4 = 8
8 = 8
From the tests, we find that only Student #3's solution (4, 1) satisfies the equation 3x - 4y = 8. Therefore, Student #3 is the one who found the correct solution.