Question
Given the equation 8x−3y=2x+9y , which of the following statements is correct?(1 point) Responses 8, −3, 2, and 9 are constants. 8, negative 3 , 2, and 9 are constants. 8, −3, 2, and 9 are coefficients. 8, negative 3 , 2, and 9 are coefficients. There are four variables. There are four variables. 8 is the only factor of 8x.
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GPT-4o mini
To analyze the equation \(8x - 3y = 2x + 9y\), we first clarify the roles of the numbers present in this equation.
1. **Constants** are values that do not change. In the context of an equation with variables, constants would typically be standalone numbers (like 5, -7, etc.). In this case, 8, -3, 2, and 9 are not constants; instead, they describe the coefficients of the variables.
2. **Coefficients** are numerical factors that multiply the variables in an equation. In your equation:
- \(8\) is the coefficient of \(x\) in \(8x\)
- \(-3\) is the coefficient of \(y\) in \(-3y\)
- \(2\) is the coefficient of \(x\) in \(2x\)
- \(9\) is the coefficient of \(y\) in \(9y\)
From this analysis, we can conclude that the correct statements would be:
- \(8\), \(-3\), \(2\), and \(9\) are coefficients.
- or, alternatively, \(8\), negative \(3\), \(2\), and \(9\) are coefficients (depending on preferred notation).
Additionally, there are only two variables involved in the equation: \(x\) and \(y\).
Finally, \(8\) is certainly one factor of \(8x\) as it is the coefficient multiplied with the variable \(x\).
Considering these clarifications, the most accurate and relevant statement is:
**8, −3, 2, and 9 are coefficients.**
1. **Constants** are values that do not change. In the context of an equation with variables, constants would typically be standalone numbers (like 5, -7, etc.). In this case, 8, -3, 2, and 9 are not constants; instead, they describe the coefficients of the variables.
2. **Coefficients** are numerical factors that multiply the variables in an equation. In your equation:
- \(8\) is the coefficient of \(x\) in \(8x\)
- \(-3\) is the coefficient of \(y\) in \(-3y\)
- \(2\) is the coefficient of \(x\) in \(2x\)
- \(9\) is the coefficient of \(y\) in \(9y\)
From this analysis, we can conclude that the correct statements would be:
- \(8\), \(-3\), \(2\), and \(9\) are coefficients.
- or, alternatively, \(8\), negative \(3\), \(2\), and \(9\) are coefficients (depending on preferred notation).
Additionally, there are only two variables involved in the equation: \(x\) and \(y\).
Finally, \(8\) is certainly one factor of \(8x\) as it is the coefficient multiplied with the variable \(x\).
Considering these clarifications, the most accurate and relevant statement is:
**8, −3, 2, and 9 are coefficients.**
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