If (k+2,3k+2) is a solution of the linear equation 3x-5y=13, then find the value of k.

Answer

To find the value of \( k \) given that \( (k+2, 3k+2) \) is a solution of the linear equation \( 3x - 5y = 13 \), we can follow these steps:

### Step 1: Substitute the values of \( x \) and \( y \)

We know that the point \( (k+2, 3k+2) \) is a solution to the equation. Therefore, we can substitute \( x = k + 2 \) and \( y = 3k + 2 \) into the equation \( 3x - 5y = 13 \).

\[ 3(k + 2) - 5(3k + 2) = 13 \]

### Step 2: Expand the equation

Now, we will expand both terms in the equation:

\[ 3(k + 2) = 3k + 6 \]
\[ -5(3k + 2) = -15k - 10 \]

Putting these into the equation gives:

\[ 3k + 6 - 15k - 10 = 13 \]

### Step 3: Combine like terms

Next, we combine the like terms on the left side:

\[ (3k - 15k) + (6 - 10) = 13 \]
\[ -12k - 4 = 13 \]

### Step 4: Isolate \( k \)

Now, we will isolate \( k \) by first adding 4 to both sides:

\[ -12k = 13 + 4 \]
\[ -12k = 17 \]

Next, divide both sides by -12:

\[ k = \frac{-17}{12} \]

### Final Answer

Thus, the value of \( k \) is:

\[ k = -\frac{17}{12} \]

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