Sistem Persamaan Linear Tiga Variabel

3x - y + 2z = 15 .....pers 1

2x + y + z = 13 ..... pers 2

3x + 2y + 2z = 24 .....pers 3

Eleminasi pers l dan 2

3x - y + 2z = 15

2x + y + z = 13

--------------------- (+)

5x + 3z = 28 ..... pers 4

Eleminasi pers l dan 3

3x - y + 2z = 15 |×2|

3x + 2y + 2z = 24|×1|

6x - 2y + 4z = 30

3x + 2y + 2z = 24

-------------------------- (+)

9x + 6z = 54 ...... pers 5

Eleminasi pers 4 dan 5

5x + 3z = 28 |×2|

9x + 6z = 54 |×1|

10x + 6z = 56

9x + 6z = 54

------------------- (-)

x = 2

Subtitusi x ke pers 4

5x + 3z = 28

5 (2) + 3z = 28

10 + 3z = 28

3z = 28 - 10

3z = 18

z = 18/3

z = 6

Subtitusi x dan z ke pers 2

2x + y + z = 13

2 (2) + y + 6 = 13

4 + y + 6 = 13

10 + y = 13

y = 13 - 10

y = 3

Maka Himpunan penyelesaian sistem persamaan linear tiga variabel tersebut adalah; HP = {(x, y, z)}

HP = {(2, 3, 6)}