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

Question

Responses

There are four variables.
There are four variables.

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

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. There are four variables.
   This statement is incorrect. The equation has two variables: \( x \) and \( y \).

2. 8, −3, 2, and 9 are constants.
   This statement is also incorrect. While 8, -3, 2, and 9 are numerical values, in the context of the equation they are part of the coefficients of the variables.

3. 8, −3, 2, and 9 are coefficients.
   This statement is correct. In the expression, 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 \( 9y \).

4. 8 is the only factor of 8x.
   This statement is misleading. While 8 is a coefficient in front of \( x \), the variable \( x \) itself is also a factor of \( 8x \).

Based on the analysis, the correct statement is:

8, −3, 2, and 9 are coefficients.