1. **State the problem:** Solve the system of linear equations: $$y = x + 3$$ $$2x + y = 11$$ 2. **Use substitution method:** Since $y$ is already expressed in terms of $x$ from the first equation, substitute $y = x + 3$ into the second equation. 3. **Substitute and simplify:** $$2x + (x + 3) = 11$$ $$2x + x + 3 = 11$$ $$3x + 3 = 11$$ 4. **Isolate $x$:** $$3x = 11 - 3$$ $$3x = 8$$ $$x = \frac{8}{3}$$ 5. **Find $y$ using $y = x + 3$:** $$y = \frac{8}{3} + 3$$ $$y = \frac{8}{3} + \frac{9}{3}$$ $$y = \frac{17}{3}$$ 6. **Final answer:** $$\boxed{\left(\frac{8}{3}, \frac{17}{3}\right)}$$ This means the solution to the system is $x = \frac{8}{3}$ and $y = \frac{17}{3}$, the point where the two lines intersect.