4. A version of the "IS-LM" macroeconomic model leads to the system of equations I(r) = S(Y) and aY + L(r) = M, where a is a positive parameter, while I, S, and L are given, continuously differentiable functions. Suppose that the system defines Y and r implicitly as differentiable functions of a and M. Find expressions for aY /AM and ar/aM