Question
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.
. 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.
Answers
GPT-4o mini
To determine which student found the correct solution to the equation \(3x - 4y = 8\), we will test each proposed solution by plugging the values of \(x\) and \(y\) into the equation.
1. **Student #1: Linda (1, -4)**
\[
3(1) - 4(-4) = 3 - (-16) = 3 + 16 = 19 \quad \text{(not equal to 8)}
\]
2. **Student #2: Nathan (5, 3)**
\[
3(5) - 4(3) = 15 - 12 = 3 \quad \text{(not equal to 8)}
\]
3. **Student #3: Gary (4, 1)**
\[
3(4) - 4(1) = 12 - 4 = 8 \quad \text{(equal to 8, correct solution)}
\]
Thus, the only student who found the correct solution is **Student #3**.
**Student #3 is correct.**
1. **Student #1: Linda (1, -4)**
\[
3(1) - 4(-4) = 3 - (-16) = 3 + 16 = 19 \quad \text{(not equal to 8)}
\]
2. **Student #2: Nathan (5, 3)**
\[
3(5) - 4(3) = 15 - 12 = 3 \quad \text{(not equal to 8)}
\]
3. **Student #3: Gary (4, 1)**
\[
3(4) - 4(1) = 12 - 4 = 8 \quad \text{(equal to 8, correct solution)}
\]
Thus, the only student who found the correct solution is **Student #3**.
**Student #3 is correct.**