Given the equation 8x−3y=2x+9y , which of the following statements is correct?(1 point)

Question

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.

Answer 1

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.