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, −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 . There are four variables.

Answer 1

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

1. Coefficients are the numerical factors that multiply the variables in an equation.

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

   So, the coefficients in the equation are 8, -3, 2, and 9.

2. Constants are numbers that do not multiply any variables. In this equation, there are no standalone constants present.

Based on these definitions and observations, the correct statement is:

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

Therefore, the correct response is: 8, -3, 2, and 9 are coefficients.