Answer:
(a, b, c) = (0, -4, 4)
Step-by-step explanation:
Any of a variety of calculators, spreadsheets, or web sites can solve these equations for you. A calculator result is attached. It shows the solution to be ...
(a, b, c) = (0, -4, 4)
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If you'd like to solve the system by hand, here's one way:
Add the three equations together:
(2a +b +c) +(2b +c +a) +(2c +a +b) = (0) +(-4) +(4)
4a +4b +4c = 0 . . . . simplify
a +b +c = 0 . . . . . divide by 4
Substitute this into each of the other equations:
a +(a +b +c) = 0 ⇒ a +0 = 0 ⇒ a = 0
b +(a +b +c) = -4 ⇒ b +0 = -4 ⇒ b = -4
c +(a +b +c) = 4 ⇒ c +0 = 4 ⇒ c = 4
