Assume That an Economy Is Characterized by the Following Equations $I S$

Assume that an economy is characterized by the following equations:
C = 100 + (2/3)(Y - T)
T = 600
G = 500
I = 800 - (50/3)r
M^s/P = M^d/P = 0.5Y - 50r

a. Write the numerical $I S$ curve for the economy, expressing $Y$ as a numerical function of $G , T$ , and $r$ .
b. Write the numerical $L M$ curve for this economy, expressing $r$ as a function of $Y$ and $M / P$ .
c. Solve for the equilibrium values of $Y$ and $r$ , assuming $P = 1.0$ and $M = 1,200$ . How do they change when $P = 2.0$ ? Check by computing $C , I$ , and $G$ .
d. Write the numerical aggregate demand curve for this economy, expressing $Y$ as a function of $G , T$ , and $M / P$ .