1. **State the problem:** Solve the system of equations: $$x = 3y + 11$$ $$2x - 3y = 16$$ 2. **Substitute the expression for $x$ from the first equation into the second equation:** $$2(3y + 11) - 3y = 16$$ 3. **Distribute and simplify:** $$6y + 22 - 3y = 16$$ 4. **Combine like terms:** $$3y + 22 = 16$$ 5. **Isolate $y$ by subtracting 22 from both sides:** $$3y + \cancel{22} - \cancel{22} = 16 - 22$$ $$3y = -6$$ 6. **Divide both sides by 3 to solve for $y$:** $$\frac{3y}{\cancel{3}} = \frac{-6}{\cancel{3}}$$ $$y = -2$$ 7. **Substitute $y = -2$ back into the first equation to find $x$:** $$x = 3(-2) + 11$$ $$x = -6 + 11$$ $$x = 5$$ **Final answer:** $$x = 5, \quad y = -2$$