1. **State the problem:** We need to find the solution to the system of equations: $$y = 4x - 16$$ $$4x - y = 16$$ 2. **Use substitution or elimination:** Since the first equation is already solved for $y$, substitute $y = 4x - 16$ into the second equation. 3. **Substitute:** $$4x - (4x - 16) = 16$$ 4. **Simplify inside the parentheses:** $$4x - 4x + 16 = 16$$ 5. **Simplify the left side:** $$0x + 16 = 16$$ which simplifies to $$16 = 16$$ 6. **Interpret the result:** Since the equation is always true, the two equations represent the same line. 7. **Conclusion:** The system has infinitely many solutions. **Final answer:** B. infinitely many solutions