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 .

There are four variables.
There are four variables.

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

8, −3, 2, and 9 are constants.

Answer 1

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

1. 8 is the only factor of 8x.

2. 8 is the only factor of 8 x. (This is the same statement as the first, just with a space.)

   Both of these statements are incorrect. While 8 is a factor of \( 8x \), it is not the only factor—1 is also a factor.

3. There are four variables.

   This statement is incorrect. The equation contains two variables: \( x \) and \( y \).

4. 8, −3, 2, and 9 are coefficients.

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

5. 8, −3, 2, and 9 are constants.

   This statement is incorrect. Coefficients are not constants; they are multipliers of the variables in this context.

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