1. **State the problem:** Solve the system of equations for $x$ and $y$: $$x = 14 - 4y$$ $$x + y = 5$$ 2. **Choose a method:** We will use substitution since $x$ is already expressed in terms of $y$ in the first equation. 3. **Substitute $x$ from the first equation into the second:** $$ (14 - 4y) + y = 5 $$ 4. **Simplify the equation:** $$ 14 - 4y + y = 5 $$ $$ 14 - 3y = 5 $$ 5. **Isolate $y$:** $$ -3y = 5 - 14 $$ $$ -3y = -9 $$ 6. **Divide both sides by $-3$:** $$ y = \frac{-9}{\cancel{-3}} \cancel{-3} = 3 $$ 7. **Substitute $y = 3$ back into the first equation to find $x$:** $$ x = 14 - 4(3) $$ $$ x = 14 - 12 $$ $$ x = 2 $$ **Final answer:** $$ x = 2, \quad y = 3 $$ This means the solution to the system is the point $(2, 3)$ where both equations intersect.