1. **State the problem:** Solve the system of linear equations: $$6x + 2y = 6$$ $$3x + y = 4$$ 2. **Formula and rules:** We can solve this system using substitution or elimination. Here, elimination is convenient. 3. **Step 1: Simplify the second equation:** $$3x + y = 4$$ Multiply both sides by 2 to align with the first equation's $2y$ term: $$2 \times (3x + y) = 2 \times 4$$ $$6x + 2y = 8$$ 4. **Step 2: Subtract the first equation from this new equation:** $$\cancel{6x} + 2y = 8$$ $$- (\cancel{6x} + 2y = 6)$$ ------------------- $$0 = 2$$ 5. **Interpretation:** The statement $0 = 2$ is false, meaning the system has no solution. 6. **Conclusion:** The lines are parallel and do not intersect. **Final answer:** No solution (the system is inconsistent).