Given the equation 8x−3y=2x+9y

Question

, which of the following statements is correct?(1 point)
Responses

There are four variables.
There are four variables.

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

8 is the only factor of 8x
.
8 is the only factor of 8 x .

8, −3
, 2, and 9 are coefficients.

Answer 1

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

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

2. Constants: The numbers \( 8, -3, 2, \) and \( 9 \) are not constants; they are coefficients of the variables \( x \) and \( y \) in the equation.

3. Factors: The term \( 8x \) has only the coefficient \( 8 \). Saying that \( 8 \) is the only factor is misleading because it is the coefficient of \( x \), but there’s also the variable \( x \) itself.

4. Coefficients: The terms \( 8 \) and \( -3 \) are coefficients of \( x \) and \( y \) in the first part of the equation \( 8x - 3y \). The terms \( 2 \) and \( 9 \) are coefficients of \( x \) and \( y \) in the second part of the equation \( 2x + 9y \).

Based on this analysis, the correct statement is:

8, −3, 2, and 9 are coefficients.