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