Three simple equations xzy

X-2y + 2z = -1
2x + y-z = 3
3x + 2y + z = 2

Correct answer:

x = 1
y = 0
z = -1

x - 2 y + 2 z = - 1 2 x + y - z = 3 3 x + 2 y + z = 2 x - 2 \cdot y + 2 \cdot z = - 1 2 \cdot x + y - z = 3 3 \cdot x + 2 \cdot y + z = 2 x - 2 y + 2 z = - 1 2 x + y - z = 3 3 x + 2 y + z = 2 P i v o t : R o w 1 \leftrightarrow R o w 3 3 x + 2 y + z = 2 2 x + y - z = 3 x - 2 y + 2 z = - 1 R o w 2 - \frac{2}{3} \cdot R o w 1 \to R o w 2 3 x + 2 y + z = 2 - 0.333 y - 1.667 z = 1.667 x - 2 y + 2 z = - 1 R o w 3 - \frac{1}{3} \cdot R o w 1 \to R o w 3 3 x + 2 y + z = 2 - 0.333 y - 1.667 z = 1.667 - 2.667 y + 1.667 z = - 1.667 P i v o t : R o w 2 \leftrightarrow R o w 3 3 x + 2 y + z = 2 - 2.667 y + 1.667 z = - 1.667 - 0.333 y - 1.667 z = 1.667 R o w 3 - \frac{- 0 . 3 3 3 3 3 3 3 3}{- 2 . 6 6 6 6 6 6 6 7} \cdot R o w 2 \to R o w 3 3 x + 2 y + z = 2 - 2.667 y + 1.667 z = - 1.667 - 1.875 z = 1.875 z = \frac{1 . 8 7 5}{- 1 . 8 7 5} = - 1 y = \frac{- 1 . 6 6 6 6 6 6 6 7 - 1 . 6 6 6 6 6 6 6 6 6 6 6 6 7 z}{- 2 . 6 6 6 6 6 6 6 7} = \frac{- 1 . 6 6 6 6 6 6 6 7 - 1 . 6 6 6 6 6 6 6 7 \cdot ( - 1 )}{- 2 . 6 6 6 6 6 6 6 7} = - 0 x = \frac{2 - 2 y - z}{3} = \frac{2 - 2 \cdot - 0 + 1}{3} = 1 x = 1 y = - 0 z = - 1

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