Given the equation 8x−3y=2x+9y , which of the following statements is correct?(1 point) Responses 8, −3, 2, and 9 are constants. 8, negative 3 , 2, and 9 are constants. 8, −3, 2, and 9 are coefficients. 8, negative 3 , 2, and 9 are coefficients. There are four variables. There are four variables. 8 is the only factor of 8x.

Answer 1

To analyze the equation \(8x - 3y = 2x + 9y\), we first clarify the roles of the numbers present in this equation.

1. Constants are values that do not change. In the context of an equation with variables, constants would typically be standalone numbers (like 5, -7, etc.). In this case, 8, -3, 2, and 9 are not constants; instead, they describe the coefficients of the variables.

2. Coefficients are numerical factors that multiply the variables in an equation. In your equation:

   • \(8\) is the coefficient of \(x\) in \(8x\)
   • \(-3\) is the coefficient of \(y\) in \(-3y\)
   • \(2\) is the coefficient of \(x\) in \(2x\)
   • \(9\) is the coefficient of \(y\) in \(9y\)

From this analysis, we can conclude that the correct statements would be:

• \(8\), \(-3\), \(2\), and \(9\) are coefficients.
• or, alternatively, \(8\), negative \(3\), \(2\), and \(9\) are coefficients (depending on preferred notation).

Additionally, there are only two variables involved in the equation: \(x\) and \(y\).

Finally, \(8\) is certainly one factor of \(8x\) as it is the coefficient multiplied with the variable \(x\).

Considering these clarifications, the most accurate and relevant statement is:

8, −3, 2, and 9 are coefficients.