Consider two equations describing the relationship between three variables X, 1'}, and l": X = a + b n, (I) x = c d 11., (2) where a, b, c, and d, are positive, known constants (numbers). The objective is to find values ofX, 1",, and J"; for which both equations are satised and as well 1'; = l'}. a. How many unknown variables are there? lClearly identify them. How many equations are there? Clearly identify them. Note that there should be as many equations as unknown variables. When this is the case. a unique solution exists. {Try to convince yourselfthat having only (I) and (2) makes it impossible to solve for the unknown variables, by equating X from (I) to X from (2) and trying to solve for Y] and Y2.) Replace both sides of the third equation {which one is it?) using expressions (1) and (2) to solve for X. b. After solving for X, find the values of Y: and Y: and verify whether the third equation is satised. c. Now, rename 1', as Q" representing quantity supplied, replace a with 200, replace :5 with 2, rename l': as Q\" representing quantity supplied. replace r: with 400, replace d widi 3, and rename X as P representing price. This gives you a system of supply and delnand for a good. Rewrite expressions (1) and [2) using this information. How many unknown variables and how many equations do you have? cl. To nd the equilibrium and solve for equilibrium values of Q\