Tentukan himpunan penyelesaian dari spltv 2x+y-3z=-5 X-y+z=3 3x+2y+z=16

(i) 2x + y - 3z = -5
(ii) x - y + z = 3
(iii) 3x + 2y + z = 16

Eliminasi (i) dan (ii)
2x + y - 3z = -5 |x1|
x - y + z = 3 |x3|

2x + y - 3z = -5
3x - 3y + 3z = 9
---------------------- +
5x - 2y = 4
10 - 2y = 4
-2y = -6
y = 3

Eliminasi (ii) dan (iii)
x - y + z = 3
3x + 2y + z = 16
---------------------- —
-2x - 3y = -13

5x - 2y = 4 |x3|
-2x - 3y = -13 |x2|

15x - 6y = 12
-4x - 6y = -26
------------------- —
19x = 38
x = 2

2x + y - 3z = -5
4 + 3 - 3z = -5
-3z = -5 - 4 - 3
-3z = -12
z = 4

Jadi, x = 2
y = 3
z = 4