Tentukan himpunan penyelesaian dari sistem persamaan di linier tiga variabel 2x - 3y - z = 20 X + 2y + z = 26 X + 4y + 2z = 15

2x - 3y - z = 20
x + 2y + z = 26
x + 4y + 2z = 15


persamaan 1 & 2

2x - 3y - z = 20
x + 2y + z = 26
____________+
3x - y = 46 (… 1)


persamaan 1 & 3

2x - 3y - z = 20 |×2|
x + 4y + 2z = 15 |×1|

4x - 6y - 2z = 40
x + 4y + 2z = 15
_____________+
5x - 2y = 55 (… 2)

(… 1) & (… 2)

3x - y = 46 |×2|
5x - 2y = 55 |×1|

6x - 2y = 92
5x - 2y = 55
__________-
x = 37


substitusi x = 37

3x - y = 46
3.37 - y = 46
111 - y = 46
-y = 46 - 111
-y = -65
y = 65


substitusi x = 37 y = 65

x + 4y + 2z = 15
37 + 4.65 + 2z = 15
37 + 260 + 2z = 15
297 + 2z = 15
2z = 15 - 297
2z = -282
z = -141

Eliminasi pers i dan ii
2x - 3y - z =20
x + 2y + z =26
_____________-
x + y = -6 ... (iv)

Eliminasi pers ii dan iii
x + 2y + z =26 |×2| 2x + 4y + 2z =52
x + 4y + 2z =15 |x1 | x + 4y + 2z =15
________________________-
X = 33

Substitusi pers iv
X + y = -6
33 + y =-6
y = -39

Substitusi pers ii
x + 2y + z = 26
33 + 2(39) + z = 26
33 + 78 + z = 26
Z = 26 - 33 -78
Z = -85

Hp { 33,39,-85 }