If the two lines of regression are `3x - 2y+1 = 0 and 2x -y-2=0` , then `bar x+bary` is equal to:

Options

A. 5
B. 8
C. 13
D. 3

Answer

To solve the problem, we need to find the values of \(\bar{x}\) and \(\bar{y}\) from the given lines of regression and then calculate \(\bar{x} + \bar{y}\).

### Step-by-Step Solution:

1. **Write the equations of the lines of regression:**
The given lines of regression are:
\[ 3x - 2y + 1 = 0 \quad \text{(1)} \]
\[ 2x - y - 2 = 0 \quad \text{(2)} \]

2. **Rearrange the equations:**
Rearranging the first equation:
\[ 3x - 2y = -1 \quad \text{(1')} \]
Rearranging the second equation:
\[ 2x - y = 2 \quad \text{(2')} \]

3. **Multiply the second equation to eliminate \(y\):**
Multiply equation (2') by 2:
\[ 4x - 2y = 4 \quad \text{(3)} \]

4. **Subtract equation (1') from equation (3):**
Now, we will subtract equation (1') from equation (3):
\[ (4x - 2y) - (3x - 2y) = 4 - (-1) \]
This simplifies to:
\[ 4x - 3x = 4 + 1 \]
\[ x = 5 \]

5. **Substitute \(x\) back to find \(y\):**
Substitute \(x = 5\) into equation (1'):
\[ 3(5) - 2y = -1 \]
\[ 15 - 2y = -1 \]
\[ -2y = -1 - 15 \]
\[ -2y = -16 \]
\[ y = 8 \]

6. **Calculate \(\bar{x} + \bar{y}\):**
Now, we have \(\bar{x} = 5\) and \(\bar{y} = 8\).
\[ \bar{x} + \bar{y} = 5 + 8 = 13 \]

### Final Answer:
\[ \bar{x} + \bar{y} = 13 \]