1. **State the problem:** Solve the system of equations: $$x = 2y + 1$$ $$x + y = 7$$ 2. **Use substitution method:** Since the first equation gives $x$ in terms of $y$, substitute $x = 2y + 1$ into the second equation. 3. **Substitute and simplify:** $$ (2y + 1) + y = 7 $$ Combine like terms: $$ 2y + 1 + y = 7 $$ $$ 3y + 1 = 7 $$ 4. **Isolate $y$:** $$ 3y = 7 - 1 $$ $$ 3y = 6 $$ Divide both sides by 3: $$ \cancel{3}y = \frac{6}{\cancel{3}} $$ $$ y = 2 $$ 5. **Find $x$ using $y=2$:** $$ x = 2(2) + 1 $$ $$ x = 4 + 1 $$ $$ x = 5 $$ 6. **Solution:** The solution to the system is $$ (x, y) = (5, 2) $$ This means the two lines intersect at the point $(5, 2)$.