In a bivariate distribution the regression equation of y on x is
`8x – 10y + 66 = 0.` If `barx= 13`, find `bary`

Answer

To solve the problem, we need to find the value of \( \bar{y} \) given the regression equation of \( y \) on \( x \) and the mean value of \( x \) (which is \( \bar{x} = 13 \)).

### Step-by-Step Solution:

1. **Write down the regression equation:**
The regression equation of \( y \) on \( x \) is given as:
\[ 8x - 10y + 66 = 0 \]

2. **Substitute \( \bar{x} \) into the equation:**
We know that \( \bar{x} = 13 \). We will substitute \( x \) with \( \bar{x} \) in the regression equation:
\[ 8(13) - 10\bar{y} + 66 = 0 \]

3. **Calculate \( 8 \times 13 \):**
\[ 8 \times 13 = 104 \]
So the equation becomes:
\[ 104 - 10\bar{y} + 66 = 0 \]

4. **Combine the constant terms:**
Now, combine \( 104 \) and \( 66 \):
\[ 104 + 66 = 170 \]
Thus, the equation simplifies to:
\[ 170 - 10\bar{y} = 0 \]

5. **Rearrange the equation to solve for \( \bar{y} \):**
Move \( 10\bar{y} \) to the right side:
\[ 170 = 10\bar{y} \]

6. **Divide both sides by 10:**
\[ \bar{y} = \frac{170}{10} = 17 \]

### Final Answer:
Thus, the value of \( \bar{y} \) is:
\[ \bar{y} = 17 \]