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

Question

Responses

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.

8 is the only factor of 8x.

Answer 1

In the given equation \( 8x - 3y = 2x + 9y \), let's analyze the statements:

1. 8, −3, 2, and 9 are coefficients.

2. 8, negative 3, 2, and 9 are coefficients.
   Both of these statements are indeed correct. Coefficients are the numbers multiplying the variables, so in this case:

   • 8 is the coefficient of \( x \) in \( 8x \).
   • -3 is the coefficient of \( y \) in \( -3y \).
   • 2 is the coefficient of \( x \) in \( 2x \).
   • 9 is the coefficient of \( y \) in \( 9y \).

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

4. 8, −3, 2, and 9 are constants.
   This statement is incorrect. Constants are values that do not change and are not multiplied by a variable.

5. 8 is the only factor of 8x.
   This statement is misleading. While 8 is a factor, \( x \) itself is part of the expression \( 8x \), making it a product, not simply a factor.

Based on the analysis, the correct responses are the first two statements about coefficients:

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