Solve the system of equations $$ax + 2y = b$$ and $$2x - y = 3$$ for all real values of $$a$$ and $$b$$.

PLACEHOLDER ANSWER - the answer depends on cases. From the second equation $$y = 2x - 3$$, so the first becomes $$(a + 4)x = b + 6$$. If $$a \ne -4$$, the unique solution is $$x = \frac{b + 6}{a + 4}$$, $$y = \frac{2b - 3a}{a + 4}$$. If $$a = -4$$ and $$b = -6$$, there are infinitely many solutions $$(x, 2x - 3)$$; if $$a = -4$$ and $$b \ne -6$$, there is no solution.