If the two lines of regression are `3x+y=15 and x+4y=3`, then value of x when `y=3` is

Options

A. `-4`
B. `-8`
C. 4
D. none of these

Answer

To solve the problem, we need to find the value of \( x \) when \( y = 3 \) using the two lines of regression given by the equations \( 3x + y = 15 \) and \( x + 4y = 3 \).

### Step-by-Step Solution:

1. **Substitute \( y = 3 \) into the first equation:**
\[ 3x + y = 15 \]
Substitute \( y = 3 \):
\[ 3x + 3 = 15 \]

2. **Solve for \( x \):**
\[ 3x = 15 - 3 \]
\[ 3x = 12 \]
\[ x = \frac{12}{3} = 4 \]

3. **Now substitute \( y = 3 \) into the second equation:**
\[ x + 4y = 3 \]
Substitute \( y = 3 \):
\[ x + 4(3) = 3 \]
\[ x + 12 = 3 \]

4. **Solve for \( x \):**
\[ x = 3 - 12 \]
\[ x = -9 \]

### Conclusion:
The value of \( x \) when \( y = 3 \) is \( 4 \) from the first equation and \( -9 \) from the second equation.