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

1 answer

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

  1. Coefficients: In the equation, \(8\) is the coefficient of \(x\) in \(8x\), \(-3\) is the coefficient of \(y\) in \(-3y\), \(2\) is the coefficient of \(x\) in \(2x\), and \(9\) is the coefficient of \(y\) in \(9y\). Therefore, the correct statement regarding coefficients is: "8, -3, 2, and 9 are coefficients."

  2. Constants: A constant is a value that does not change and does not have a variable associated with it. In this equation, the values \(8\), \(-3\), \(2\), and \(9\) are not constants because they are associated with variables \(x\) and \(y\). Hence, the statements about these being constants are not correct.

  3. Factors: The term "factors" is primarily used in the context of multiplication. Thus, the statements about \(8\) being the "only factor of \(8x\)" or "8 is the only factor of 8 x" are misleading because it is a coefficient, not necessarily a factor in the traditional sense.

  4. Variables: In the given equation, there are only two variables, \(x\) and \(y\). Therefore, the statement "There are four variables" is incorrect.

Based on this analysis, the correct statement is: "8, -3, 2, and 9 are coefficients."