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

8, −3, 2, and 9 are constants.

Answer 1

To analyze the equation \( 8x - 3y = 2x + 9y \), we first identify the various components:

1. Variables: In this equation, the variables are \(x\) and \(y\). There are two variables, not four.

2. Coefficients: In the equation, the coefficients are the numbers multiplying the variables:

   • For \(8x\), the coefficient is \(8\).
   • For \(-3y\), the coefficient is \(-3\).
   • For \(2x\), the coefficient is \(2\).
   • For \(9y\), the coefficient is \(9\).

   Therefore, the numbers \(8, -3, 2,\) and \(9\) are all coefficients.

3. Constants: A constant is a number that does not change and does not multiply a variable. In this case, there are no constants explicitly in the equation since all numbers are associated with variables.

Given these analyses, the correct statement is:

8, −3, 2, and 9 are coefficients.