If `(1)/(8)x+(1)/(8)y=y-2x`, then what is the value of `(x)/(y)`?

Answer

To solve the equation \( \frac{1}{8}x + \frac{1}{8}y = y - 2x \) and find the value of \( \frac{x}{y} \), we can follow these steps:

### Step 1: Rewrite the equation
Start with the given equation:
\[ \frac{1}{8}x + \frac{1}{8}y = y - 2x \]

### Step 2: Factor out \( \frac{1}{8} \) from the left-hand side
We can factor out \( \frac{1}{8} \) from the left-hand side:
\[ \frac{1}{8}(x + y) = y - 2x \]

### Step 3: Multiply both sides by 8
To eliminate the fraction, multiply both sides of the equation by 8:
\[ x + y = 8(y - 2x) \]

### Step 4: Distribute on the right-hand side
Distributing the 8 on the right-hand side gives:
\[ x + y = 8y - 16x \]

### Step 5: Rearrange the equation
Now, rearrange the equation to get all terms involving \( x \) on one side and all terms involving \( y \) on the other side:
\[ x + 16x = 8y - y \]
This simplifies to:
\[ 17x = 7y \]

### Step 6: Solve for \( \frac{x}{y} \)
Now, we can express \( \frac{x}{y} \):
\[ \frac{x}{y} = \frac{7}{17} \]

Thus, the value of \( \frac{x}{y} \) is:
\[ \frac{x}{y} = \frac{7}{17} \]