Answer:
(x, y, z) = (4, -3, 2)
Step-by-step explanation:
I. -2x + y + 6z = 1
II. 3x + 2y + 5z = 16
III. 7x + 3y - 4z = 11
use I and II. cancel out a variable
-2(-2x + y + 6z = 1)
3x + 2y + 5z = 16
+ (4x - 2y - 12z = -2)
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IV. 7x - 7z = 14
use I and III. cancel out the same variable (y)
-3(-2x + y + 6z = 1)
7x + 3y - 4z = 11
+ (6x - 3y - 18z = -3)
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V. 13x - 22z = 8
use IV and V. cancel out a variable
13(7x - 7z = 14)
-7(13x - 22z = 8)
91x - 91z = 182
+(-91x + 154z = -56)
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63z = 126
divide by 63
z = 2
plug z into IV
7x - 7z = 14
7x - 7(2) = 14
7x - 14 = 14
7x = 28
x = 4
plug x and z into I
-2x + y + 6z = 1
-2(4) + y + 6(2) = 1
-8 + y + 12 = 1
y + 4 = 1
y = -3
(x, y, z) = (4, -3, 2)
