2x - 2y + z = 5....multiply by -1
2x - 2y + 3z = 7
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-2x + 2y - z = -5 (result of multiplying by -1)
2x - 2y + 3z = 7
-------------------add
2z = 2
z = 2/2 = 1
2x - 2y + z = 5.....multiply by 3
-3x - 3y + 3z = 9...multiply by 2
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6x - 6y + 3z = 15 (result of multiplying by 3)
-6x - 6y + 6z = 18 (result of multiplying by 2)
-------------------add
-12y + 9z = 33
-12y + 9(1) = 33
-12y + 9 = 33
-12y = 33 - 9
-12y = 24
y = -24/12
y = -2
2x - 2y + z = 5
2x - 2(-2) + 1 = 5
2x + 4 + 1 = 5
2x + 5 = 5
2x = 5 - 5
2x = 0
x = 0
solution is : (0,-2,1)