Question

Given the equation 8x−3y=2x+9y, which of the following statements is correct?(1 point)%0D%0AResponses%0D%0A%0D%0A8, −3, 2, and 9 are coefficients.%0D%0A8, negative 3 , 2, and 9 are coefficients.%0D%0A%0D%0A8, −3, 2, and 9 are constants.%0D%0A8, negative 3 , 2, and 9 are constants.%0D%0A%0D%0A8 is the only factor of 8x.%0D%0A8 is the only factor of 8 x .%0D%0A%0D%0AThere are four variables.

Answer 1

To analyze the given equation \(8x - 3y = 2x + 9y\), let's first identify the coefficients and constants.

1. **Coefficients**:
- The coefficients of the terms involving variables are the numbers multiplying the variables:
- In \(8x\), the coefficient of \(x\) is \(8\).
- In \(-3y\), the coefficient of \(y\) is \(-3\).
- In \(2x\), the coefficient of \(x\) is \(2\).
- In \(9y\), the coefficient of \(y\) is \(9\).
- Therefore, the coefficients in the equation are \(8\), \(-3\), \(2\), and \(9\).

2. **Constants**:
- There are no constant terms (i.e., numbers without variables) in the equation, so \(8\), \(-3\), \(2\), and \(9\) are not constants.

3. **Factors**:
- In the term \(8x\), the number \(8\) is a coefficient, not the only factor of \(8x\) since \(8 = 8 \cdot 1\).
- Hence, \(8\) is not the only factor of \(8x\).

4. **Variables**:
- The variables in the equation are \(x\) and \(y\).
- There are only two variables, not four.

Now, looking at the statements provided:

1. "8, −3, 2, and 9 are coefficients." - This statement is **correct**.
2. "8, negative 3, 2, and 9 are coefficients." - This statement is also **correct**, as it uses the word "negative" instead of the symbol.
3. "8, −3, 2, and 9 are constants." - This statement is **incorrect**.
4. "8, negative 3, 2, and 9 are constants." - This statement is also **incorrect**.
5. "8 is the only factor of 8x." - This statement is **incorrect**.
6. "There are four variables." - This statement is **incorrect**.

The correct responses are the first and the second statements regarding the coefficients.