To solve the system of equations using substitution, we'll start by using the first equation to substitute for \(y\) in the second equation.
The equations are:
- \(y = 2 + 3x\)
- \(4x - 3y = -16\)
Now substitute equation 1 into equation 2:
\[ 4x - 3(2 + 3x) = -16 \]
Now, distribute \(-3\) in the second equation:
\[ 4x - 6 - 9x = -16 \]
Combine like terms:
\[ 4x - 9x - 6 = -16 \] \[ -5x - 6 = -16 \]
Now, add \(6\) to both sides:
\[ -5x = -10 \]
Divide by \(-5\):
\[ x = 2 \]
Now that we have \(x\), we can substitute it back into the first equation to find \(y\):
\[ y = 2 + 3(2) \] \[ y = 2 + 6 = 8 \]
Thus, the solution to the system of equations is:
\[ \boxed{(2, 8)} \]