Question
Given the equation 8 x minus 3 y equals 2 x plus 9 y, which of the following statements is correct?
Answers
Answer
here are the choices 1: 8 is the only factor of 8x. 2: there are four variables 3: 8,-3,2, and 9 are coefficients. 4: 8,-3,2, and 9 are constants.
Answered by
GPT-4o mini
To analyze the equation \( 8x - 3y = 2x + 9y \), we can first rearrange it to find a relationship between \( x \) and \( y \).
1. Start by bringing all terms involving \( x \) on one side and terms involving \( y \) on the other side.
\[
8x - 2x = 9y + 3y
\]
This simplifies to:
\[
6x = 12y
\]
2. Next, we can simplify this equation:
\[
x = 2y
\]
This shows the relationship between \( x \) and \( y \). Now, we can address the potential statements you might have about this equation. Generally correct options might include:
- \( x \) is directly proportional to \( y \)
- When \( y = 0 \), \( x = 0 \)
- The slope of \( x \) in terms of \( y \) is 2
- Any line through the origin dependent on the ratio of \( x \) to \( y \) being 2.
If you provide specific statements from which to evaluate, I can definitively determine which one is correct!
1. Start by bringing all terms involving \( x \) on one side and terms involving \( y \) on the other side.
\[
8x - 2x = 9y + 3y
\]
This simplifies to:
\[
6x = 12y
\]
2. Next, we can simplify this equation:
\[
x = 2y
\]
This shows the relationship between \( x \) and \( y \). Now, we can address the potential statements you might have about this equation. Generally correct options might include:
- \( x \) is directly proportional to \( y \)
- When \( y = 0 \), \( x = 0 \)
- The slope of \( x \) in terms of \( y \) is 2
- Any line through the origin dependent on the ratio of \( x \) to \( y \) being 2.
If you provide specific statements from which to evaluate, I can definitively determine which one is correct!
Answered by
GPT-4o mini
Let's analyze the choices given the equation \( 8x - 3y = 2x + 9y \).
1. **8 is the only factor of 8x.**
This statement is incorrect. While 8 is a factor of \( 8x \), \( x \) itself can take on any value, meaning there are infinitely many factors (for example, \( 1 \), \( 2 \), \( 4 \), etc. for any non-zero \( x \)).
2. **There are four variables.**
This statement is also incorrect. In the equation \( 8x - 3y = 2x + 9y \), there are only two variables, \( x \) and \( y \).
3. **8, -3, 2, and 9 are coefficients.**
This statement is correct. 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 \( 9y \).
4. **8, -3, 2, and 9 are constants.**
This statement is incorrect. Constants are values that do not change (like a standalone number). In this case, \( 8 \), \(-3\), \( 2 \), and \( 9 \) are indeed numbers, but in the context of the equation, they act as coefficients of the variables \( x \) and \( y \).
Based on the evaluation, the correct statement is:
**3: 8, -3, 2, and 9 are coefficients.**
1. **8 is the only factor of 8x.**
This statement is incorrect. While 8 is a factor of \( 8x \), \( x \) itself can take on any value, meaning there are infinitely many factors (for example, \( 1 \), \( 2 \), \( 4 \), etc. for any non-zero \( x \)).
2. **There are four variables.**
This statement is also incorrect. In the equation \( 8x - 3y = 2x + 9y \), there are only two variables, \( x \) and \( y \).
3. **8, -3, 2, and 9 are coefficients.**
This statement is correct. 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 \( 9y \).
4. **8, -3, 2, and 9 are constants.**
This statement is incorrect. Constants are values that do not change (like a standalone number). In this case, \( 8 \), \(-3\), \( 2 \), and \( 9 \) are indeed numbers, but in the context of the equation, they act as coefficients of the variables \( x \) and \( y \).
Based on the evaluation, the correct statement is:
**3: 8, -3, 2, and 9 are coefficients.**
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