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

Question

Responses

8 is the only factor of 8x.
8 is the only factor of 8 x .

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

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

There are four variables.

Answer 1

Let's analyze the equation \( 8x - 3y = 2x + 9y \) and the provided statements:

1. 8 is the only factor of 8x.

   • This is not accurate. While 8 is a factor, \( x \) would also be considered a factor.

2. 8 is the only factor of 8 x.

   • This is the same statement as the first one, and it is also false for the same reason.

3. 8, −3, 2, and 9 are coefficients.

   • This statement is true. In the equation, 8 is the coefficient of \( x \), -3 is the coefficient of \( y \), 2 is the coefficient of \( x \) (after moving it to the left side), and 9 is the coefficient of \( y \). So, they are all coefficients.

4. 8, −3, 2, and 9 are constants.

   • This statement is false. Coefficients are not constants; they multiply the variables.

5. There are four variables.

   • This statement is also false. There are two variables in the equation—\( x \) and \( y \).

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