1. **State the problem:** Solve the system of linear equations: $$y = x + 1$$ $$2x + 3y = 4$$ 2. **Use substitution method:** Since the first equation gives $y$ in terms of $x$, substitute $y = x + 1$ into the second equation. 3. **Substitute and simplify:** $$2x + 3(x + 1) = 4$$ $$2x + 3x + 3 = 4$$ $$5x + 3 = 4$$ 4. **Isolate $x$:** $$5x = 4 - 3$$ $$5x = 1$$ 5. **Solve for $x$:** $$x = \frac{1}{5}$$ 6. **Find $y$ using $y = x + 1$:** $$y = \frac{1}{5} + 1 = \frac{1}{5} + \frac{5}{5} = \frac{6}{5}$$ 7. **Final answer:** The solution to the system is $$\boxed{\left(\frac{1}{5}, \frac{6}{5}\right)}$$ This means the two lines intersect at the point $\left(\frac{1}{5}, \frac{6}{5}\right)$.