To solve the system of equations using substitution, we start with the two equations given:
- \( x = 3y + 8 \) (Equation 1)
- \( 5x + 3y = 22 \) (Equation 2)
Since Equation 1 already gives \( x \) in terms of \( y \), we can substitute this expression for \( x \) into Equation 2.
Substituting \( x \) in Equation 2:
\[ 5(3y + 8) + 3y = 22 \]
Now, distribute \( 5 \):
\[ 15y + 40 + 3y = 22 \]
Combine like terms:
\[ 18y + 40 = 22 \]
Next, isolate \( y \) by subtracting \( 40 \) from both sides:
\[ 18y = 22 - 40 \] \[ 18y = -18 \]
Now, divide both sides by \( 18 \):
\[ y = -1 \]
Now that we have \( y \), we can substitute it back into Equation 1 to find \( x \):
\[ x = 3(-1) + 8 \] \[ x = -3 + 8 \] \[ x = 5 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (5, -1) \]
Final Solution: \[ \boxed{(5, -1)} \]