Question

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

Answer 1

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

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

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

   • The coefficient of \(x\) on the left side is \(8\) and on the right side is \(2\).
   • The coefficient of \(y\) on the left side is \(-3\) and on the right side is \(9\).

   Thus, the numbers \(8, -3, 2, 9\) are indeed coefficients.

3. Constants: A constant is a number that does not change and does not multiply any variables. In this case, there are no standalone constant terms in the equation since all numbers are associated with the variables. Therefore, \(8, -3, 2, 9\) are not constants.

4. Factors: The only factor of \(8x\) is \(8\) when considering \(8\) as the coefficient of the variable \(x\), but also \(x\) itself is a factor of \(8x\).

Based on the analysis:

• The correct statement is: "8, −3, 2, and 9 are coefficients."