(a) first equation x + 2y - 3z = 11
(b) second equation 2x + y - 2z = 9
(c) third equation 4x + 3y +z = 16
1) let's eliminate x from (a) and (b)
multiply (a) by - 2 → -2x -4y +3z = -22 and add it to b):
-2x - 4y +6z = -22
2x + y -2z = 9
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0x -3y +4z = - 13 → -3y + 4z = -13 (d)
2) Now eliminate x from b) and c)
multiply b) by -2 → -4x - 2y +4z = - 18 and add it to c):
-4x - 2y + 4z = -18
4x + 3y + z = 16
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0x + y + 5z = -2 → y+ 5z = -2 (e)
3) Now we have 2 equations with 2 variables:
(d) -3y + z = -13
(e) y+ 5z = -2
4) again eliminate y from (d) and (3). by
multiplying (e) by 3 → 3y +15 z = -6 (f).
Add d) to f):
e) -3y + 4z = -13
f) 3y +15 z = -6
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0y + 19z = - 19 and z = -1
Now replace z by - 1 , starting from the last pair of equation and up, you will find:
x = 2, y = 3 and z = -1
