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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 constants.
8, negative 3 , 2, and 9 are constants.

There are four variables.
There are four variables.

8, −3, 2, and 9 are coefficients.

1 answer

To analyze the equation \( 8x - 3y = 2x + 9y \) and determine which statement is correct, let's look closely at the options:

  1. "8 is the only factor of 8x." - This is not accurate because in the expression \( 8x \), \( x \) is also considered a factor.

  2. "8 is the only factor of 8 x." - Similar to the previous statement, \( x \) is also a factor.

  3. "8, −3, 2, and 9 are constants." - This statement is incorrect; the numbers mentioned are coefficients of variables, not constants.

  4. "8, −3, 2, and 9 are constants." - This is identical to the previous option, so it remains incorrect.

  5. "There are four variables." - In the equation, there are only two variables: \( x \) and \( y \).

  6. "8, −3, 2, and 9 are coefficients." - This statement is correct. 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 \( 9y \).

Based on this analysis, the correct statement is:

"8, −3, 2, and 9 are coefficients."