Himpunan penyelesaian dari SPLTV: 2x+y-3z=-5, x-y+z=3, 3x+2y+z=16
Matematika
ratnaw976
Pertanyaan
Himpunan penyelesaian dari SPLTV: 2x+y-3z=-5, x-y+z=3, 3x+2y+z=16
1 Jawaban
-
1. Jawaban BSunShine
Materi : SPLTV
Kelas : X SMA
2x + y - 3z = -5 ........... 1)
x - y + z = 3 ................. 2)
3x + 2y + z = 16 .......... 3)
2x + y - 3z = -5 ....... ×1
x - y + z = 3 ........ ×2
-------------------------------
2x + y - 3z = -5
2x - 2y + 2z = 6
------------------------------(-)
3y - 5z = -11
x - y + z = 3 ............. ×3
3x + 2y + z = 16 ...... ×1
--------------------------------
3x - 3y + 3z = 9
3x + 2y + z = 16
-------------------------------- (-)
-5y + 2z = -7
3y - 5z = -11 ...... ×5
-5y + 2z = -7 ..... ×(-3)
-----------------------------
15y - 25z = -55
15y - 6z = 21
---------------------- (-)
-19z = -76
z = 4
3y - 5z = -11
3y - 5(4) = -11
3y - 20 = -11
3y = -11 + 20
3y = 9
y = 3
x - y + z = 3
x - 3 + 4 = 3
x + 1 = 3
x = 3 - 1
x = 2
Hp = { 2 , 3 , 4}