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.

There are four variables.
There are four variables.

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

Answer 1

To analyze the equation \( 8x - 3y = 2x + 9y \):

1. Coefficients: In the equation, the terms in front of the variables \( x \) and \( y \) are called coefficients. Here, \( 8 \) is the coefficient of \( x \), \( -3 \) is the coefficient of \( y \) on the left side, and \( 2 \) and \( 9 \) are the coefficients of \( x \) and \( y \) on the right side, respectively. So, the correct statement is:

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

2. Variables: The variables in the equation are \( x \) and \( y \). Therefore, there are only two variables, not four.

3. Constants: The numbers \( 8, -3, 2, \) and \( 9 \) are not constants; they are coefficients. Constants would be standalone numbers not multiplied by any variables.

Based on this analysis, the correct response from the provided options is:

8, −3, 2, and 9 are coefficients.