1. **State the problem:** Solve the system of linear equations: $$2x + y = 7$$ $$4x + 2y = 14$$ 2. **Formula and rules:** To solve a system of linear equations, we can use substitution, elimination, or matrix methods. Here, elimination is straightforward. 3. **Step 1: Simplify the second equation:** Notice the second equation is exactly twice the first: $$4x + 2y = 2(2x + y) = 2 \times 7 = 14$$ 4. **Step 2: Recognize dependency:** Since the second equation is just a multiple of the first, both represent the same line. 5. **Step 3: Express $y$ in terms of $x$ from the first equation:** $$2x + y = 7 \implies y = 7 - 2x$$ 6. **Step 4: Conclusion:** The system has infinitely many solutions along the line $y = 7 - 2x$. **Final answer:** $$\boxed{y = 7 - 2x \text{ with } x \in \mathbb{R}}$$