If `x=3k+2` and `y = 2k-1` is a solution of the equation `4x-3y+1=0`, find the value of k.

Answer

To find the value of \( k \) given that \( x = 3k + 2 \) and \( y = 2k - 1 \) is a solution of the equation \( 4x - 3y + 1 = 0 \), we will substitute the expressions for \( x \) and \( y \) into the equation and solve for \( k \).

### Step-by-Step Solution:

1. **Substitute \( x \) and \( y \) into the equation:**
\[ 4(3k + 2) - 3(2k - 1) + 1 = 0 \]

2. **Distribute the coefficients:**
\[ 12k + 8 - 6k + 3 + 1 = 0 \]

3. **Combine like terms:**
\[ (12k - 6k) + (8 + 3 + 1) = 0 \]
\[ 6k + 12 = 0 \]

4. **Isolate \( k \):**
\[ 6k = -12 \]
\[ k = \frac{-12}{6} \]
\[ k = -2 \]

### Final Answer:
The value of \( k \) is \( -2 \).

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