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. There are four variables. There are four variables. 8 is the only factor of 8x. 8 is the only factor of 8 x . 8, −3, 2, and 9 are constants.

Question

GPT-4o mini · Accepted Answer

Let's analyze the equation $8x - 3y = 2x + 9y$. 1. **Identifying Coefficients**: - In the equation, the coefficients of the variables $x$ and $y$ are obtained by looking at their respective terms: - The coefficient of $x$ in $8x$ is $8$. - The coefficient of $y$ in $-3y$ is $-3$. - The coefficient of $x$ in $2x$ is $2$. - The coefficient of $y$ in $9y$ is $9$. - Therefore, $8$, $-3$, $2$, and $9$ are indeed coefficients. 2. **Constants**: - In this equation, there are no constant terms (terms without variables), so the statement that "8, −3, 2, and 9 are constants" is incorrect. 3. **Variables**: - The variables in the equation are $x$ and $y$. Therefore, saying "there are four variables" is incorrect, as there are only two variables. 4. **Factors of a Term**: - The statement "8 is the only factor of $8x$" is misleading. While $8$ is a factor, $x$ can also be considered part of the term $8x$. There can be multiple factors of a term. Given this analysis, the correct statement is: **"8, −3, 2, and 9 are coefficients."**