Question

Substitusikan SPLTV berikut

Answer 1

Verified answer

Materi : SPLTV
Kelas : X SMA
Metode : Substitusi 

x + y + 2z = 0 .............. 1)
x - y + z = 4 ................. 2)
3x + 2y + z = 2 ........... 3)

x + y + 2z = 0 ⇔ x = -y - 2z 

x - y + z = 4
(-y - 2z) - y + z = 4
-2y - z = 4 .................. 4)

3x + 2y + z = 2
3(-y - 2z) + 2y + z = 2
-3y - 6z + 2y  +z = 2
-y - 5z = 2 ................... 5)

-2y - z = 4 ....... × (-1)
-y - 5z = 2 ....... × (-2)
-----------------------------
2y + z = -4
2y + 10z = -4
----------------------------- (-)
-9z = 0
z = 0

-2y - z = 4
-2y - 0 = 4
-2y = 4
y = -2

x - y + z = 4
x - (-2) + 0 = 4
x + 2 + 0 = 4
x = 4 - 2
x = 2

Hp = { 2 , -2 , 0 }