If `(3, - 1)` is a solution of the linear equation `4x -ky = 8x + 2y`, then find the value of `k`.

Options

A. 11
B. 13
C. 10
D. 15

Answer

To find the value of \( k \) in the equation \( 4x - ky = 8x + 2y \) given that \( (3, -1) \) is a solution, we will substitute \( x = 3 \) and \( y = -1 \) into the equation.

### Step-by-Step Solution:

1. **Substitute the values of \( x \) and \( y \)**:
\[ 4(3) - k(-1) = 8(3) + 2(-1) \]

2. **Calculate the left-hand side**:
\[ 4(3) = 12 \quad \text{and} \quad -k(-1) = k \]
So, the left-hand side becomes:
\[ 12 + k \]

3. **Calculate the right-hand side**:
\[ 8(3) = 24 \quad \text{and} \quad 2(-1) = -2 \]
So, the right-hand side becomes:
\[ 24 - 2 = 22 \]

4. **Set the left-hand side equal to the right-hand side**:
\[ 12 + k = 22 \]

5. **Solve for \( k \)**:
\[ k = 22 - 12 \]
\[ k = 10 \]

Thus, the value of \( k \) is \( 10 \).