3x+y-z=-2 2x-3y+32=17 4x-y+2z=12

// Sistem Persamaan Linear Tiga Variabel //

Eliminasi persamaan 1 dan 2

3x + y – z = – 2 [ × 3 ]
2x – 3y + 3z = 17 [ × 1 ]

9x + 3y – 3z = – 6
2x – 3y + 3z = 17
———————— +
11x = 11
x = 1

Eliminasi persamaan 1 dan 3

3x + y – z = – 2
4x – y + 2z = 12
——————— +
7x + z = 10 (persamaan 4)

Substitusi x = 1 ke persamaan 4

7x + z = 10
7(1) + z = 10
7 + z = 10
z = 10 – 7
z = 3

Substitusi x = 1 dan z = 3 ke persamaan 1

3x + y – z = – 2
3(1) + y – (3) = – 2
3 + y – 3 = – 2
y = – 2 – 3 + 3
y = – 2

Maka, himpunan penyelesaian :

{ x , y , z } = { 1 , – 2 , 3 }