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 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.

Answer 1

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

1. There are four variables.

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

2. 8 is the only factor of \( 8x \).

   • This statement is technically correct but somewhat misleading since \( 8x \) can be factored as \( 8 \cdot x \). However, "the only factor" usually implies there are no other factors at play, which isn't entirely the case as we can consider \( 1 \) as a factor of \( 8x \).

3. 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 \( 9y \).

4. 8, −3, 2, and 9 are constants.

   • This statement is incorrect. Coefficients are not considered constants; constants are typically defined as values without variables attached.

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