Question
Given the equation 8x−3y=2x+9y , which of the following statements is correct?(1 point)
Responses
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.
8, negative 3 , 2, and 9 are constants.
8, −3, 2, and 9 are coefficients.
Responses
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.
8, negative 3 , 2, and 9 are constants.
8, −3, 2, and 9 are coefficients.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To analyze the equation \( 8x - 3y = 2x + 9y \) and the statements provided, let's define key terms:
- **Variables**: Typically, the symbols representing unknowns, in this case \( x \) and \( y \).
- **Constants**: Fixed numerical values that do not change.
- **Coefficients**: The numerical factor in front of variables.
Now let's evaluate the statements:
1. **There are four variables.**
- This statement is **incorrect**. There are only two variables: \( x \) and \( y \).
2. **8 is the only factor of 8x.**
- This statement is **misleading**. While 8 is a factor of \( 8x \), \( x \) itself is also a factor since \( 8x = 8 \cdot x \). Therefore, it's not accurate to say 8 is the only factor.
3. **8, −3, 2, and 9 are constants.**
- This statement is **incorrect**. The numbers \( 8, -3, 2, \) and \( 9 \) are coefficients of the variables \( x \) and \( y \), not constants.
4. **8, −3, 2, and 9 are coefficients.**
- This statement is **correct**. In the equation, \( 8 \) is the coefficient of \( x \), \( -3 \) is the coefficient of \( y \) on the left side, and \( 2 \) and \( 9 \) are coefficients of \( x \) and \( y \) respectively on the right side.
The correct statement is:
**8, −3, 2, and 9 are coefficients.**
- **Variables**: Typically, the symbols representing unknowns, in this case \( x \) and \( y \).
- **Constants**: Fixed numerical values that do not change.
- **Coefficients**: The numerical factor in front of variables.
Now let's evaluate the statements:
1. **There are four variables.**
- This statement is **incorrect**. There are only two variables: \( x \) and \( y \).
2. **8 is the only factor of 8x.**
- This statement is **misleading**. While 8 is a factor of \( 8x \), \( x \) itself is also a factor since \( 8x = 8 \cdot x \). Therefore, it's not accurate to say 8 is the only factor.
3. **8, −3, 2, and 9 are constants.**
- This statement is **incorrect**. The numbers \( 8, -3, 2, \) and \( 9 \) are coefficients of the variables \( x \) and \( y \), not constants.
4. **8, −3, 2, and 9 are coefficients.**
- This statement is **correct**. In the equation, \( 8 \) is the coefficient of \( x \), \( -3 \) is the coefficient of \( y \) on the left side, and \( 2 \) and \( 9 \) are coefficients of \( x \) and \( y \) respectively on the right side.
The correct statement is:
**8, −3, 2, and 9 are coefficients.**
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