Tentukan himpunan penyelesaian dari persamaan tiga variabel x - 2y + 3z = 6, 2x - y + 2z = 4, dan x - y + 2z = 2!

x - 2y + 3z = 6
2x - y + 2z = 4
x - y + 2z = 2


persamaan 1 & 2

x - 2y + 3z = 6 |×2|
2x - y + 2z = 4 |×1|

2x - 4y + 6z = 12
2x - y + 2z = 4
_____________-
-3y + 4z = 8 (… 1)


persamaan 1 & 3

x - 2y + 3z = 6
x - y + 2z = 2
___________-
-y + z = 4 (… 2)


(…1) & (…2)

-3y + 4z = 8 |×1|
-y + z = 4 |×3|

-3y + 4z = 8
-3y + 3z = 12
__________-
z = -4


substitusi z = -4

-y + z = 4
-y + (-4) = 4
-y = 4 + 4
-y = 8
y = -8


substitusi z = -4 y = -8

x - y + 2z = 2
x - (-8) + 2(-4) = 2
x + 8 - 8 = 2
x = 2