Q. Aggregate demand in the IS-LM model?

Aggregate demand

As investments depend on R and consumption and imports depend on Y, aggregate demand will rely on both Y and R. In cross model, we used notation Y_D(Y) for aggregate demand. In IS-LM model, we should instead use the notation Y_D(Y, R). Now We have 

Y_D(Y, R) = C(Y) + I(R) + G + X - Im(Y)

It doesn't make much of a difference if we allow C and Im to depend on R as well, Y_D will rely positively on Y and negatively on R in any case.

It must also be clear that we can no longer determine GDP the way we did it in cross model. We can't successfully solve the equation Y_D(Y, R) = Y since we have only one equation and two unknowns (Y and R). We need one additional equation if we want to solve for both Y and R. This equation would come from the money market.