Question

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

Answer 1

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 \( 1.5x - 2y = 8 \).