To find the value of \( k \), substitute the given values of \( x = 2 \) and \( y = 1 \) into the equation:
\[ 2x + 3y = k \]
Substituting \( x = 2 \) and \( y = 1 \):
\[ 2(2) + 3(1) = k \]
\[ 4 + 3 = k \]
\[ k = 7 \]
Thus, the value of \( k \) is \( 7 \).