Question

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

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.

There are four variables.
There are four variables.

8 is the only factor of 8x.

Answer 1

Let's analyze the equation \( 8x - 3y = 2x + 9y \).

The numbers 8, -3, 2, and 9 are associated with the terms involving the variables \( x \) and \( y \). In this context:

- **Coefficients** are numbers multiplied by the variables (e.g., in \( 8x \), 8 is the coefficient of \( x \)).
- **Constants** are standalone numbers without variables.

Given this, let's look at the statements:

1. "8, −3, 2, and 9 are constants." - This is incorrect.
2. "8, negative 3, 2, and 9 are constants." - This is incorrect.
3. "8, −3, 2, and 9 are coefficients." - This is correct.
4. "8, negative 3, 2, and 9 are coefficients." - This is also correct.
5. "There are four variables." - This is incorrect. There are only two variables (\( x \) and \( y \)).
6. "8 is the only factor of 8x." - This is incorrect because \( 8x \) can be factored as \( 8 \cdot x \).

Thus, the correct answers from the statements provided are:

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

Both of these statements about coefficients are accurate.