spltv 2x + 3y + 3z = 4 2x - 6y + 9z = 5 4x - 3z = 4

Mapel : Matematika
Kelas : X SMA
Bab : SPLTV

Pembahasan :
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2x + 3y + 3z = 4 ..... (1)
2x - 6y + 9z = 5 ..... (2)
4x - 3z = 4 .............. (3)

Eliminasi (1) dan (2)
(1) 2x + 3y + 3z = 4 (kali 2)
=> 4x + 6y + 6z = 8
(2) 2x - 6y + 9z = 5
-------------------------- +
... 6x + 15z = 13 ........ (4)

Eliminasi (3) dan (4)
(3) 4x - 3z = 4 (kali 5)
=> 20x - 15z = 20
(4) 6x + 15z = 13
-------------------------- +
26x = 33
x = 33/26

(3) 4x - 3z = 4
=> 4(33/26) - 3z = 4
=> 66/13 - 4 = 3z
=> 14/13 = 3z
=> z = 14/39

2x + 3y + 3z = 4
2(33/26) + 3y + 3(14/39) = 4
33/13 + 3y + 14/13 = 4
47/13 + 3y = 4
3y = 4 - 47/13
3y = 5/13
y = 5/39

HP = {33/26, 5/39, 14/39}