These equations are called the structural equations of the IS-LM model. Notice that the structural equations show the dependent variables, Y and i, as functions of each other. They have to be solved simultaneously to find the equilibrium solution, which can either be done using substitution or by using Cramer's Rule as shown in the Appendix. The solution takes the form of the reduced form equations:
The reduced form equations show the endogenous variables as functions of exogenous variables and parameters. The asterisk ( * ) denotes the equilibrium value of a variable. Notice that using consolidating parameters gets rid of a lot of clutter, but we do lose an immediate sense of how the underlying parameters affect these solutions. It is a good exercise to work out the effect of changes in key exogenous variables on the consolidating parameters and on the reduced form equations.