1. **State the problem:** Solve the system of equations: $$8x + 4y = 12$$ $$y = -2x + 3$$ 2. **Use substitution method:** Since the second equation gives $y$ in terms of $x$, substitute $y = -2x + 3$ into the first equation. 3. **Substitute and simplify:** $$8x + 4(-2x + 3) = 12$$ $$8x - 8x + 12 = 12$$ 4. **Simplify further:** $$\cancel{8x} - \cancel{8x} + 12 = 12$$ $$12 = 12$$ 5. **Interpret the result:** The equation $12 = 12$ is always true, meaning the two equations represent the same line. 6. **Conclusion:** There are infinitely many solutions because the system represents the same line. **Final answer:** Infinitely many solutions.