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Solve each system of equations 2a+b+c=0 2b+c+a=-4 2c+a+b+4

User Losnir
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1 Answer

10 votes

Answer:

(a, b, c) = (0, -4, 4)

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

Solve each system of equations 2a+b+c=0 2b+c+a=-4 2c+a+b+4-example-1
User Wonil
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