1. **Problem Statement**: Given the demand function $Q^D_x = 800 - 0.6P_x$ and the supply function $Q^S_x = 200 + 0.4P_x$, find the market equilibrium price and quantity. 2. **Set Demand equal to Supply to find equilibrium**: $$800 - 0.6P_x = 200 + 0.4P_x$$ 3. **Solve for $P_x$ (price):** Move all $P_x$ terms to one side: $$800 - 200 = 0.4P_x + 0.6P_x$$ $$600 = 1.0P_x$$ So, $$P_x = 600$$ 4. **Find equilibrium quantity by substituting $P_x=600$ into either function:** Using demand function: $$Q^D_x = 800 - 0.6 imes 600 = 800 - 360 = 440$$ 5. **Verify with supply function:** $$Q^S_x = 200 + 0.4 imes 600 = 200 + 240 = 440$$ 6. **Conclusion:** The market equilibrium price is $600$, and the equilibrium quantity is $440$.