1. **State the problem:** Solve the system of linear equations: $$\begin{cases} 2x - 4y = -3 \\ x - 2y = 1 \end{cases}$$ 2. **Use substitution or elimination method.** Here, notice the second equation is simpler: $$x - 2y = 1$$ 3. **Express $x$ from the second equation:** $$x = 1 + 2y$$ 4. **Substitute $x$ into the first equation:** $$2(1 + 2y) - 4y = -3$$ 5. **Simplify:** $$2 + 4y - 4y = -3$$ 6. **Cancel terms:** $$2 + \cancel{4y} - \cancel{4y} = -3$$ 7. **Simplify further:** $$2 = -3$$ 8. **Interpretation:** This is a contradiction, meaning no values of $y$ satisfy the system. 9. **Conclusion:** The system has no solution; the lines are parallel and do not intersect. **Final answer:** No solution (the system is inconsistent).