1) x - 2y + 3z = -3
2) 2x - 3y - z = 7
3) 3x + y -2z = 6
multiply eq(3) by 2, add to eq(1):
x - 2y + 3z = -3
6x + 2y - 4z = 12
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7x - z = 9 (a)
multiply eq(3) by 3, add to eq(2):
2x - 3y - z = 7
9x + 3y - 6z = 18
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11x - 7z = 25 (b)
multiply eq(a) by -7, add to eq(b):
-49x + 7z = -63
11x - 7z = 25
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-38x = -38
x = -38/-38 = 1
using eq(a):
7(1) - z = 9
-z = 2
z = -2
using eq(2):
2(1) - 3y - (-2) = 7
2 - 3y + 2 = 7
-3y = 3
y = 3/-3 = -1
check using eq(1):
x - 2y + 3z = -3
1 - 2(-1) + 3(-2) = -3
1 + 2 - 6 = -3
-3 = -3
x = 1, y = -1, z = -2 or (1, -1, -2)