Suppose there are only two goods - Food (F) and Shelter (S). The demand equations for these two goods depend on their prices, pF and pS as follows:

DF (pF, pS) = 10-2pF-pS

DS (pF,pS) = 10-pF-2pS

The supply curves depend only on their own prices:

SF (pF) = pF

SS (pS) = 5pS

Determine the equilibrium price and quantity of these goods. Show ALL work