Sistem persamaan linear 3 variabel: 2x + 3y - z = 20 3x + 2y + z = 20 x + 4y + 2z = 15

2x + 3y - z = 20
3x + 2y + z = 20
----------------------- +
5x + 5y = 40

3x + 2y + z = 20 || ×2
x + 4y + 2z = 15 || ×1
------------------------------
6x + 4y + 2z = 40
x + 4y + 2z = 15
--------------------------- -
5x = 25
x = 5

5x + 5y = 40
5(5) + 5y = 40
25 + 5y = 40
5y = 15
y = 3

2x + 3y - z = 20
2(5) + 3(3) - z = 20
10 + 9 - z = 20
z = -1

2x + 3y - z = 20 pers(1)
3x + 2y + z = 20 pers(2)
x + 4y + 2z = 15 pers(3)

eliminasikan pers (1) dan (2)
2x + 3y - z = 20
3x + 2y + z = 20
tambahkan
5x + 5y = 40
atau
x + y = 8 pers(4)


eliminasikan pers (2) dan (3)
sebelumnya pers(3)
x + 4y + 2z = 15 bagi 2 kedua ruas
½x + 2y + z = 15/2

jadi
½x + 2y + z = 15/2
3x + 2y + z = 20
kurangkan
-5/2x = (15/2 - 20)
-5/2x = -25/2
x = (-25/2) x (-2/5)
x=-25/-5
x=5

x + y = 8
y = 8-5
y = 3

2x + 3y -z =20
2(5)+3(3)-z=20
-z=20-19
-z=1
z=-1
jadi nilai x y z ={ 5,3,-1}