`x+2y=3`
`2x-y=8.5`
If `(x, y)` is a solution to the above system of equtions, what is the value of `x-y`?

Answer

To solve the system of equations given by:

1. \( x + 2y = 3 \) (Equation 1)
2. \( 2x - y = 8.5 \) (Equation 2)

we will follow these steps:

### Step 1: Make the coefficients of \( x \) the same
To do this, we can multiply Equation 1 by 2:

\[ 2(x + 2y) = 2(3) \]

This gives us:

\[ 2x + 4y = 6 \quad \text{(Equation 3)} \]

### Step 2: Write down Equation 2
We will keep Equation 2 as it is:

\[ 2x - y = 8.5 \quad \text{(Equation 2)} \]

### Step 3: Subtract the two equations
Now we will subtract Equation 2 from Equation 3:

\[ (2x + 4y) - (2x - y) = 6 - 8.5 \]

This simplifies to:

\[ 2x + 4y - 2x + y = 6 - 8.5 \]

Which further simplifies to:

\[ 5y = -2.5 \]

### Step 4: Solve for \( y \)
Now we can solve for \( y \):

\[ y = \frac{-2.5}{5} = -0.5 \quad \text{or} \quad y = -\frac{1}{2} \]

### Step 5: Substitute \( y \) back to find \( x \)
Now we substitute \( y \) back into Equation 1 to find \( x \):

\[ x + 2(-\frac{1}{2}) = 3 \]

This simplifies to:

\[ x - 1 = 3 \]

Thus,

\[ x = 3 + 1 = 4 \]

### Step 6: Find \( x - y \)
Now we have \( x = 4 \) and \( y = -\frac{1}{2} \). We need to find \( x - y \):

\[ x - y = 4 - (-\frac{1}{2}) = 4 + \frac{1}{2} = 4.5 \]

### Final Answer
Thus, the value of \( x - y \) is:

\[ \boxed{4.5} \]

---