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.
8 is the only factor of 8 x .

Answer 1

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

1. There are four variables.

   • This statement is incorrect. The variables in the equation are \( x \) and \( y \). There are only two variables.

2. 8, −3, 2, and 9 are constants.

   • This statement is also incorrect. While these numbers are constant values, they are not constants in the context of the equation. Instead, they are coefficients of the variables. Constants are typically independent of variables.

3. 8, −3, 2, and 9 are coefficients.

   • This statement is correct. In the equation, the numbers \( 8 \), \( -3 \), \( 2 \), and \( 9 \) serve as coefficients for the variables \( x \) and \( y \).

4. 8 is the only factor of 8x.

   • This statement is misleading. While \( 8 \) is a factor of \( 8x \), it is not the only factor, as any multiple of \( x \) multiplied by \( 8 \) would also be a factor (e.g., \( 4x \times 2 \)).

Therefore, the correct statement is:

8, −3, 2, and 9 are coefficients.