Consider a two-commodity market. When the unit prices of the products are $P_1$ and $P_2$, the quantities demanded, $D_1$ and $D_2$, and the quantities supplied, $S_1$ and $S_2$, are given by $$\begin{array}{r@{}r@{}r@{}r@{}r@{}r@{}r} D_1 & = & 182 & - & 3 P_1 & - & P_2 \\ D_2 & = & 165 & - & P_1 & - & 2 P_2 \\ & & & & & & \\ S_1 & = & - 68 & + & 3 P_1 & & \\ S_2 & = & - 41 & & & + & 3 P_2 \end{array}$$ (a) What is the relationship between the two commodities? Do they compete, as do Volvos and BMWs, or do they complement one another, as do shirts and ties?
choose compete complement

(b) Find the equilibrium prices (i.e. the prices for which supply equals demand), for both products.
$P_1=$ $P_2=$