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.

Answer 1

To analyze the equation \( 8x - 3y = 2x + 9y \), we can identify the constants, coefficients, and variables.

1. Identifying the constants and coefficients:

   • Constants are fixed values and do not change. In the equation, the numbers \(8\), \(-3\), \(2\), and \(9\) are all numeric values.
   • Coefficients are the factors that multiply variables. Here, \(8\) 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 \(9y\).

2. Variables: There are two variables present in the equation, which are \(x\) and \(y\).

Given the statements:

• "8, −3, 2, and 9 are constants." (Incorrect; they are coefficients)
• "8, negative 3, 2, and 9 are constants." (Incorrect; they are coefficients)
• "8, −3, 2, and 9 are coefficients." (Correct)
• "8 is the only factor of 8x." (Incorrect; factors could include \(8\) and \(x\) or \(8\) itself)
• "There are four variables." (Incorrect; there are only two variables, \(x\) and \(y\))

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