To solve the system of equations using substitution, we start with the two given equations:
- \( x + 2y = 7 \) (Equation 1)
- \( 2x - y = -16 \) (Equation 2)
First, solve Equation 1 for \( x \):
\[ x = 7 - 2y \]
Now that we have \( x \) in terms of \( y \), we can substitute this expression for \( x \) into Equation 2:
\[ 2(7 - 2y) - y = -16 \]
Now distribute the \( 2 \):
\[ 14 - 4y - y = -16 \]
Combine like terms:
\[ 14 - 5y = -16 \]
Next, isolate \( y \) by subtracting 14 from both sides:
\[ -5y = -16 - 14 \] \[ -5y = -30 \]
Now, divide both sides by -5:
\[ y = \frac{-30}{-5} = 6 \]
Now that we have the value of \( y \), we can substitute it back into the expression we found for \( x \):
\[ x = 7 - 2(6) \] \[ x = 7 - 12 \] \[ x = -5 \]
Thus, the solution to the system of equations is
\[ x = -5, \quad y = 6 \]
So the final answer is:
\[ \boxed{(-5, 6)} \]