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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 identify the coefficients and constants.

  1. The coefficients are the numbers that multiply the variables. In the terms:
    • \(8x\) has a coefficient of 8 for \(x\).
    • \(-3y\) has a coefficient of -3 for \(y\).
    • \(2x\) has a coefficient of 2 for \(x\).
    • \(9y\) has a coefficient of 9 for \(y\).

So the coefficients in the equation are 8, -3, 2, and 9.

  1. There are no constants in this equation, as all terms are variable-based (there are no standalone numbers without variables).

  2. The statement "8 is the only factor of 8x" is misleading in the context. While 8 is indeed a factor of \(8x\), other interpretations could focus on variable factors or other aspects.

  3. There are two variables in the equation, which are \(x\) and \(y\).

From this analysis, the correct statement from the options given is:

8, -3, 2, and 9 are coefficients.