SOLUTION: SOLVE: X + Y + Z = 6 4X + 2Y + Z = 9 7X + 4Y + Z = 9

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Question 174763: SOLVE:
X + Y + Z = 6
4X + 2Y + Z = 9
7X + 4Y + Z = 9
Answer by Alan3354(69443) About Me  (Show Source):
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X + Y + Z = 6
4X + 2Y + Z = 9
7X + 4Y + Z = 9
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|1 1 1 6|
|4 2 1 9| = 0
|7 4 1 9|
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DET = 1*(2-4) -1*(4-7) + 1*(16-14) = -2 +3 +2
DET = 3
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x*DET = 1*(9-9) -1*(18-36) +6*(2-4) = 18 - 12 = 6
X = 2
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-y*DET = 1*(9-9) -1*(36-63) +6*(4-7) = 27 -18 = 9
y = -3
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z*DET = 1*(18-36) -1*(36-63) +6*(16-14) = -18 +27 +12 = 21
z = 7