Let's analyze the equation \(8x - 3y = 2x + 9y\).
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Coefficients: 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 \(9y\). Therefore, the correct statement regarding coefficients is: "8, -3, 2, and 9 are coefficients."
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Constants: A constant is a value that does not change and does not have a variable associated with it. In this equation, the values \(8\), \(-3\), \(2\), and \(9\) are not constants because they are associated with variables \(x\) and \(y\). Hence, the statements about these being constants are not correct.
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Factors: The term "factors" is primarily used in the context of multiplication. Thus, the statements about \(8\) being the "only factor of \(8x\)" or "8 is the only factor of 8 x" are misleading because it is a coefficient, not necessarily a factor in the traditional sense.
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Variables: In the given equation, there are only two variables, \(x\) and \(y\). Therefore, the statement "There are four variables" is incorrect.
Based on this analysis, the correct statement is: "8, -3, 2, and 9 are coefficients."