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

Question

Responses

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

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.

Answer 1

To analyze the equation \( 8x - 3y = 2x + 9y \):

1. Identifying Factors: The expression \( 8x \) contains the coefficient 8 multiplied by the variable \( x \). Saying "8 is the only factor of \( 8x \)" is technically correct, but \( x \) itself is also a factor. The same applies to \( 2x \). Therefore, both statements regarding the factors are not entirely accurate in the context of being the only factor.

2. Constants vs. Coefficients:

   • Constants are numbers that do not change and do not vary with the variables. In this equation, \( 8, -3, 2, \) and \( 9 \) are indeed constants.
   • Coefficients are the numerical factors in front of the variable terms in an algebraic expression. In this 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, those values are also correctly identified as coefficients.

3. Identifying Variables: The equation contains two variables: \( x \) and \( y \).

Now, evaluating the statements:

• "8 is the only factor of 8x." (Ambiguous)
• "8, −3, 2, and 9 are constants." (Correct)
• "8, −3, 2, and 9 are coefficients." (Also correct)
• "There are four variables." (Incorrect, as there are only two variables: \( x \) and \( y \))

Given this analysis, the correct statement is:

8, −3, 2, and 9 are constants.