Question

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

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 .

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

There are four variables.

Answer 1

To analyze the equation \(8x - 3y = 2x + 9y\), let's first identify the components involved. In the equation:

- \(8x\) has a coefficient of 8 (the number multiplying the variable \(x\)).
- \(-3y\) has a coefficient of -3 (the number multiplying the variable \(y\)).
- \(2x\) has a coefficient of 2.
- \(9y\) has a coefficient of 9.

Now, let's determine the truth of each response option:

1. **"8, −3, 2, and 9 are coefficients."**
- This statement is true because these numbers are indeed the coefficients of their respective variables.

2. **"8, negative 3, 2, and 9 are coefficients."**
- This statement is also true and is just a restatement of the first option with "negative" spelled out.

3. **"8 is the only factor of 8x."**
- This statement is misleading. While 8 is a factor, it is not the only one. Factors of \(8x\) can also include \(1\), \(x\), and any other number that can multiply to give \(8x\).

4. **"8, −3, 2, and 9 are constants."**
- This statement is false, as these numbers are coefficients rather than constants. Constants are fixed numbers, while coefficients are the multipliers of the variables.

5. **"There are four variables."**
- This statement is false; there are only two variables in the equation: \(x\) and \(y\).

Based on the analysis, the correct options that are true are the first two statements about coefficients.