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

Responses

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 .

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

There are four variables.

1 answer

To analyze the equation \(8x - 3y = 2x + 9y\), let's first identify the components involved. In the equation:

  • \(8x\) has a coefficient of 8 (the number multiplying the variable \(x\)).
  • \(-3y\) has a coefficient of -3 (the number multiplying the variable \(y\)).
  • \(2x\) has a coefficient of 2.
  • \(9y\) has a coefficient of 9.

Now, let's determine the truth of each response option:

  1. "8, −3, 2, and 9 are coefficients."

    • This statement is true because these numbers are indeed the coefficients of their respective variables.

  2. "8, negative 3, 2, and 9 are coefficients."

    • This statement is also true and is just a restatement of the first option with "negative" spelled out.

  3. "8 is the only factor of 8x."

    • This statement is misleading. While 8 is a factor, it is not the only one. Factors of \(8x\) can also include \(1\), \(x\), and any other number that can multiply to give \(8x\).

  4. "8, −3, 2, and 9 are constants."

    • This statement is false, as these numbers are coefficients rather than constants. Constants are fixed numbers, while coefficients are the multipliers of the variables.

  5. "There are four variables."

    • This statement is false; there are only two variables in the equation: \(x\) and \(y\).

Based on the analysis, the correct options that are true are the first two statements about coefficients.