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

Question

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.

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

There are four variables.
There are four variables.

Answer 1

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

1. Constants vs. Coefficients:

   • In the equation, \(8\), \(-3\), \(2\), and \(9\) are coefficients of the variables \(x\) and \(y\).
   • Coefficients are the numerical factors that multiply the variables, while constants are standalone numbers not multiplied by any variable.
   • Thus, statements referencing them as constants are incorrect.

2. Factors of \(8x\):

   • The term \(8x\) has \(8\) as its coefficient, and we could say that \(8\) is a factor of \(8x\) because \(8x = 8 \cdot x\).
   • However, the statement "8 is the only factor of \(8x\)" would be misleading because other factors also exist for \(8x\), such as \(4 \cdot 2 \cdot x\). Hence, this statement is incorrect.

3. Number of Variables:

   • In the equation, there are two variables: \(x\) and \(y\). Thus, the statement claiming there are four variables is incorrect.

Based on this analysis, the correct response is:

8, −3, 2, and 9 are coefficients.