Question
Giving the equation 8x - 3y = 2x + 9y which of the following statements is correct three, - 3, 2, and 9 are constants 8 is the only factor of a x there are four variables eight, minus three, two, and nine, are coefficients
Answers
GPT-4o mini
Let's analyze the equation you've provided:
\[ 8x - 3y = 2x + 9y \]
To clarify the statements based on this equation:
1. **Constants**: In the context of an equation, constants are numbers that do not change and do not contain any variables. In your equation, there are no standalone numbers on either side of the equation (like `2`, `5`, etc.). Instead, it includes numbers that are part of terms involving variables.
2. **Coefficients**: Coefficients are numbers that are multiplied by variables. In the equation:
- \( 8 \) is the coefficient of \( x \) in the term \( 8x \).
- \( -3 \) is the coefficient of \( y \) in the term \( -3y \).
- \( 2 \) is the coefficient of \( x \) in the term \( 2x \).
- \( 9 \) is the coefficient of \( y \) in the term \( 9y \).
Now, reviewing your options:
- "three, -3, 2, and 9 are constants" – This statement is **incorrect**; they are coefficients, not constants.
- "8 is the only factor of ax" – This seems incorrect as \( a \) is not defined in the context of your equation; the term involving \( x \) here is \( 8x \), not \( ax \).
- "there are four variables" – This statement is **incorrect**; there are only two variables \( x \) and \( y \).
- "eight, minus three, two, and nine are coefficients" – This statement is **correct**.
Hence, the correct statement is: **"Eight, minus three, two, and nine are coefficients."**
\[ 8x - 3y = 2x + 9y \]
To clarify the statements based on this equation:
1. **Constants**: In the context of an equation, constants are numbers that do not change and do not contain any variables. In your equation, there are no standalone numbers on either side of the equation (like `2`, `5`, etc.). Instead, it includes numbers that are part of terms involving variables.
2. **Coefficients**: Coefficients are numbers that are multiplied by variables. In the equation:
- \( 8 \) is the coefficient of \( x \) in the term \( 8x \).
- \( -3 \) is the coefficient of \( y \) in the term \( -3y \).
- \( 2 \) is the coefficient of \( x \) in the term \( 2x \).
- \( 9 \) is the coefficient of \( y \) in the term \( 9y \).
Now, reviewing your options:
- "three, -3, 2, and 9 are constants" – This statement is **incorrect**; they are coefficients, not constants.
- "8 is the only factor of ax" – This seems incorrect as \( a \) is not defined in the context of your equation; the term involving \( x \) here is \( 8x \), not \( ax \).
- "there are four variables" – This statement is **incorrect**; there are only two variables \( x \) and \( y \).
- "eight, minus three, two, and nine are coefficients" – This statement is **correct**.
Hence, the correct statement is: **"Eight, minus three, two, and nine are coefficients."**