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(1) 3x - 2y - z = 14
(2) x - 3y - 3z = 8
(3) 2x - 4y - 2z = 8
Multiply equation (2) by -3
-3(x - 3y - 3z) = -3(8)
-3x + 9y + 9z = -24
Add it to the equation (1)
(1) 3x - 2y - z = 14
-3x + 9y + 9z = -24
-------------------
(4) 7y + 8z = -10
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Multiply equation (2) by -2
-2(x - 3y - 3z) = -2(8)
-2x + 6y + 6z = -16
Add it to the equation (3)
(3) 2x - 4y - 2z = 8
-2x + 6y + 6z = -16
-------------------
2y + 4z = -8
Divide that through by 2
(5) y + 2z = -4
Now we have a system of 2 equations with only 2 unknowns:
(4) 7y + 8z = -10
(5) y + 2z = -4
Multiply eq. (5) by -4
-4(y + 2z) = -4(-4)
-4y - 8z = 16
add that to eq (4):
(4) 7y + 8z = -10
-4y - 8z = 16
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3y = 6
y = 2
Substitute in eq (4)
7(2) + 8z = -10
14 + 8z = -10
8z = -10-14
8z = -24
z = -3
Substute y = 2 and z = -3 in eq. (1)
(1) 3x - 2y - z = 14
3x - 2(2) - (-3) = 14
3x - 4 + 3 = 14
3x - 1 = 14
3x = 15
x = 5
So the solution (x,y,z) = (5,2,-3)
Edwin