1) x + 2y = 2

2) 2x + 3y - z = -9

3) 4x + 2y + 5z = 1

multiply eq(2) by 5, add to eq(3):

10x + 15y - 5z = -45

4x + 2y + 5z = 1

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14x + 17y = -44 (i)

multiply eq(1) by -14, add to eq(i):

-14x - 28y = -28

14x + 17y = -44

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-11y = -72

y = 72/11

using eq(1):

x + 2(72/11) = 2

x + 144/11 = 22/11

x = -122/11

using eq(3):

4(-122/11) + 2(72/11) + 5z = 1

-488/11 + 144/11 + 5z = 11/11

5z = 355/11

z = 71/11

check using eq(2):

2(-122/11) + 3(72/11) - 71/11 = -9

-244/11 + 216/11 - 71/11 = -99/11

-99/11 = -99/11

x = -122/11, y = 72/11, z = 71/11