Given the equation 8x−3y=2x+9y, which of the following statements is correct?(1 point)%0D%0AResponses%0D%0A%0D%0A8, −3, 2, and 9 are coefficients.%0D%0A8, negative 3 , 2, and 9 are coefficients.%0D%0A%0D%0A8, −3, 2, and 9 are constants.%0D%0A8, negative 3 , 2, and 9 are constants.%0D%0A%0D%0A8 is the only factor of 8x.%0D%0A8 is the only factor of 8 x .%0D%0A%0D%0AThere are four variables.

Question

GPT-4o mini · Answer

To analyze the given equation $8x - 3y = 2x + 9y$, let's first identify the coefficients and constants. 1. **Coefficients**: - The coefficients of the terms involving variables are the numbers multiplying the variables: - In $8x$, the coefficient of $x$ is $8$. - In $-3y$, the coefficient of $y$ is $-3$. - In $2x$, the coefficient of $x$ is $2$. - In $9y$, the coefficient of $y$ is $9$. - Therefore, the coefficients in the equation are $8$, $-3$, $2$, and $9$. 2. **Constants**: - There are no constant terms (i.e., numbers without variables) in the equation, so $8$, $-3$, $2$, and $9$ are not constants. 3. **Factors**: - In the term $8x$, the number $8$ is a coefficient, not the only factor of $8x$ since $8 = 8 \cdot 1$. - Hence, $8$ is not the only factor of $8x$. 4. **Variables**: - The variables in the equation are $x$ and $y$. - There are only two variables, not four. Now, looking at the statements provided: 1. "8, −3, 2, and 9 are coefficients." - This statement is **correct**. 2. "8, negative 3, 2, and 9 are coefficients." - This statement is also **correct**, as it uses the word "negative" instead of the symbol. 3. "8, −3, 2, and 9 are constants." - This statement is **incorrect**. 4. "8, negative 3, 2, and 9 are constants." - This statement is also **incorrect**. 5. "8 is the only factor of 8x." - This statement is **incorrect**. 6. "There are four variables." - This statement is **incorrect**. The correct responses are the first and the second statements regarding the coefficients.