To solve the system of equations using substitution, we first have the two equations:
- \( y = 2 + 3x \)
- \( 4x - 3y = -16 \)
Since the first equation already gives us \( y \) in terms of \( x \), we can substitute this expression for \( y \) into the second equation.
Substituting \( y \) in the second equation:
\[ 4x - 3(2 + 3x) = -16 \]
Now, distribute the \(-3\) to the terms inside the parentheses:
\[ 4x - 6 - 9x = -16 \]
Combine like terms:
\[ (4x - 9x) - 6 = -16 \]
This simplifies to:
\[ -5x - 6 = -16 \]
Next, add 6 to both sides:
\[ -5x = -10 \]
Now, divide both sides 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:
\[ (x, y) = (2, 8) \]
From the options provided, the correct answer is:
(2, 8).