Please show all algebraic steps.

Suppose that the demand function of a good is given by q = Yo + 9p+u, where p represents the price of the good, q represents the quantity of the good, and u represents the unobserved factors that determine the demand function. Also, let the supply of the good be, a = 00 + 81p+, where n captures the unobserved factors that determine the supply function. Let E[u] = E[n] = 0, Var(u) = 0, and Var(n) = 0. In addition assume that the unobserved components, u and n, are not correlated, that is Cov(u, n) = 0. =( [a] Solve the system of equations (demand and supply) and show that p and q depend on the unobserved components u and n. [b] Obtain the means of the price and quantity derived in part (a). [c] Obtain the variance of the price and quantity derived in part [a]. Suppose that the demand function of a good is given by q = Yo + 9p+u, where p represents the price of the good, q represents the quantity of the good, and u represents the unobserved factors that determine the demand function. Also, let the supply of the good be, a = 00 + 81p+, where n captures the unobserved factors that determine the supply function. Let E[u] = E[n] = 0, Var(u) = 0, and Var(n) = 0. In addition assume that the unobserved components, u and n, are not correlated, that is Cov(u, n) = 0. =( [a] Solve the system of equations (demand and supply) and show that p and q depend on the unobserved components u and n. [b] Obtain the means of the price and quantity derived in part (a). [c] Obtain the variance of the price and quantity derived in part [a]