1. **State the problem:** Solve the system of linear equations: $$2y + x = 3$$ $$4y + 3a = 11$$ 2. **Identify variables and equations:** The first equation involves variables $x$ and $y$, the second involves $y$ and $a$. Since $x$ and $a$ are different variables, we cannot solve for all variables simultaneously without more information. 3. **Focus on the first equation to express $x$ in terms of $y$:** $$2y + x = 3$$ $$x = 3 - 2y$$ 4. **Focus on the second equation to express $a$ in terms of $y$:** $$4y + 3a = 11$$ $$3a = 11 - 4y$$ $$a = \frac{11 - 4y}{3}$$ 5. **Summary:** The system cannot be solved for unique values of $x$, $y$, and $a$ because there are three variables but only two equations. However, we can express $x$ and $a$ in terms of $y$ as: $$x = 3 - 2y$$ $$a = \frac{11 - 4y}{3}$$ This represents the solution set parametrized by $y$.