If x =3k-2 ; y =2k is a solution of equation 4x-7y+12=0 then find the value of k

Answer

To solve the problem, we need to find the value of \( k \) such that the equations \( x = 3k - 2 \) and \( y = 2k \) satisfy the linear equation \( 4x - 7y + 12 = 0 \).

### Step-by-Step Solution:

1. **Substitute the values of \( x \) and \( y \) into the equation**:
We know that:
\[ x = 3k - 2 \]
\[ y = 2k \]
We substitute these values into the equation \( 4x - 7y + 12 = 0 \):
\[ 4(3k - 2) - 7(2k) + 12 = 0 \]

2. **Distribute the constants**:
Now we will distribute the constants in the equation:
\[ 12k - 8 - 14k + 12 = 0 \]

3. **Combine like terms**:
Combine the terms involving \( k \) and the constant terms:
\[ (12k - 14k) + (-8 + 12) = 0 \]
This simplifies to:
\[ -2k + 4 = 0 \]

4. **Isolate \( k \)**:
To find \( k \), we will isolate it:
\[ -2k = -4 \]
Dividing both sides by -2 gives:
\[ k = 2 \]

5. **Conclusion**:
The value of \( k \) that satisfies the equation is:
\[ k = 2 \]