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

8, −3, 2, and 9 are coefficients.

Answer 1

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

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 misleading. While 8 is indeed a factor of \(8x\), it is not the only factor. For example, \(1\) and \(x\) are also factors.

3. 8, −3, 2, and 9 are constants.
   This statement is incorrect. Constants are values that do not change. In the equation, 8, -3, 2, and 9 are not constants; they are coefficients of the variables \(x\) and \(y\).

4. 8, −3, 2, and 9 are coefficients.
   This statement is correct. Coefficients are numerical factors that multiply the variables in an algebraic expression. In this case, 8 is the coefficient of \(x\) in the term \(8x\), -3 is the coefficient of \(y\) in the term \(-3y\), 2 is the coefficient of \(x\) in the term \(2x\), and 9 is the coefficient of \(y\) in the term \(9y\).

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