This is a matrices problem and in particular using Cramer's Rule to solve a National Income Model.

Write the following National Income Model in the form Ax = b and solve using Cramer's Rule:

C=α+βY
I=γ+θr
Y=C+I

Where income(Y), consumption(C) and investment(I) are endogenous; the rate of interest(r) is exogenous and α, β, γ and θ are known constants.  Also find the slope of the IS curve.