Given the equation 8x−3y=2x+9y, which of the following statements is correct?(1 point)

Question

Responses

8, −3, 2, and 9 are constants.
8, negative 3 , 2, and 9 are constants.

There are four variables.
There are four variables.

8, −3, 2, and 9 are coefficients.
8, negative 3 , 2, and 9 are coefficients.

8 is the only factor of 8x.

Answer 1

To analyze the equation \(8x - 3y = 2x + 9y\), let's break down the statements provided:

1. 8, −3, 2, and 9 are constants.
   This is incorrect. These values are not constants; they are coefficients of the variables in the equation.

2. 8, negative 3, 2, and 9 are constants.
   This is also incorrect for the same reason as the first statement.

3. There are four variables.
   This is incorrect. There are only two variables in the equation: \(x\) and \(y\).

4. There are four variables.
   This statement is identical to the previous one and is also incorrect for the same reason.

5. 8, −3, 2, and 9 are coefficients.
   This statement is correct. In the equation, 8 is the coefficient of \(x\) in the term \(8x\), -3 is the coefficient of \(y\) in the term \(-3y\), 2 is the coefficient of \(x\) in \(2x\), and 9 is the coefficient of \(y\) in \(9y\).

6. 8 is the only factor of 8x.
   This statement is misleading. While 8 is the coefficient of \(x\) in \(8x\), it is not the only factor (since \(x\) can also vary).

Therefore, the correct statement is: 8, −3, 2, and 9 are coefficients.