Diketahui SPLTV 4x + 3y + z = 16 2x + 7y + 3z = 8 x – 3y – 2z = - 14 carilah himpunan penyelesaiannya

4x + 3y + z = 16....(1)
2x + 7y + 3z = 8...(2)
x - 3y - 2z = -14...(3)
○> eliminasi z dari pers. (1) &(2)
4x + 3y + z = 16|×3
2x + 7y + 3z = 8|×1
12x + 9y + 3z = 48
2x + 7y + 3z = 8
---------------------------- -
10x + 2y = 40.....(4)
○> eliminasi z dari pers. (1) & (3)
4x + 3y + z = 16|×2
x - 3y - 2z = -14|×1
8x + 6y + 2z = 32
x - 3y - 2z = -14
-------------------------- +
9x + 3y = 18....(5)
○> eliminasi y dari pers. (4) & (5)
10x + 2y = 40|×3
9x + 3y = 18|×2
30x + 6y = 120
18x + 6y = 36
---------------------- -
12x = 84
x = 84/12
x = 7
○> subtitusi x = 7 ke pers. (5)
9(7) + 3y = 18
63 + 3y = 18
3y = 18-63
y = -45/3
y = -15
○> subtitusi x=7 & y=-15 ke pers. (3)
7 - 3(-15) - 2z = -14
7 + 45 - 2z = -14
52 - 2z = -14
-2z = -14-52
z = -66/-2
z = 33
jadi, himpunan penyelesaian dari sistem pers. tsb adalah
{(7, -15, 33)}