Question 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 coefficients. 8, negative 3 , 2, and 9 are coefficients. 8, −3, 2, and 9 are constants. 8, negative 3 , 2, and 9 are constants. There are four variables. There are four variables.

Question

GPT-4o mini · Answer

Let's analyze the equation $8x - 3y = 2x + 9y$. 1. **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."** 2. **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. 3. **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. 4. **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."**