three equations in three unknowns

Find all points (a, b, c) in R^3 such that:
a(b + c) = 0
b(a + c) = 1
c(a + b) = -3
This problem, in slightly different wording, is on the web, among a set of tournament problems.
Here is the set of tournament problems (as a pdf file).
keywords: Mathematics, Number Theory, challenge