the math teacher asked his students to determine a solution for 1.5x-2y=8

1 answer

To determine a solution for the equation \( 1.5x - 2y = 8 \), you can solve for one variable in terms of the other. Here, we'll solve for \( y \) in terms of \( x \):

  1. Start with the original equation:

    \[ 1.5x - 2y = 8 \]

  2. Rearrange the equation to isolate \( y \):

    \[ -2y = 8 - 1.5x \]

  3. Divide everything by -2 to solve for \( y \):

    \[ y = \frac{1.5x - 8}{2} \]

  4. Simplify:

    \[ y = 0.75x - 4 \]

Now you have \( y \) expressed in terms of \( x \). You can choose any value for \( x \) to find a corresponding value for \( y \). Here are a few example solutions:

  • If \( x = 0 \):

    \[ y = 0.75(0) - 4 = -4 \quad \Rightarrow \quad (0, -4) \]

  • If \( x = 4 \):

    \[ y = 0.75(4) - 4 = 3 - 4 = -1 \quad \Rightarrow \quad (4, -1) \]

  • If \( x = 8 \):

    \[ y = 0.75(8) - 4 = 6 - 4 = 2 \quad \Rightarrow \quad (8, 2) \]

These points (0, -4), (4, -1), and (8, 2) are all solutions to the equation \( 1.5x - 2y = 8 \).