Kak tolong bantu jawab ya pakai caranya Himpunan penyelesaian dari sistem persamaan: 3/x + 4/y + 5/z = 4 5/x - 6/y + 1/z = 17/30 6/x + 1/y - 3/z = 21/20 adalah.

Materi: Sistem persamaan

Pembahasan d gambar
Jawaban D

3/x + 4/y + 5/z = 4
5/x - 6/y + 1/z = 17/30
6/x + 1/y - 3/z = 21/20

misal :
p = 1/x
q = 1/y
r = 1/z
3p + 4q + 5r = 4 (× 1)
5p - 6q + r = 17/30 (× 5)
...3p + 4q + 5r = 4
25p - 30q + 5r = 17/6
--------------------------------- -
- 22p + 34q = 7/6 => pers.1

3p + 4q + 5r = 4 (× 3)
6p + q - 3r = 21/20 (× 5)
..9p + 12q + 15r = 12
30p + 5q - 15r = 21/4
-------------------------------- +
39p + 17q = 69/4 => pers.2

-22p + 34q = 7/6 (× 1)
39p + 17q = 69/4 (× 2)
-22p + 34q = 7/6
78p + 34q = 69/2
-------------------------- -
- 100p = - 200/6
p = (-200/6)/-100 = 200/600 = 1/3
-22p + 34q = 7/6
-22(1/3) + 34q = 7/6
- 22/3 + 34q = 7/6
34q = 7/6 + 22/3
34q = 7/6 + 44/6
34q = 51/6
q = (51/6)/34
q = (51/6) × (1/34)
q = 51/204 = 1/4
3p + 4q + 5r = 4
3(1/3) + 4(1/4) + 5r = 4
3/3 + 4/4 + 5r = 4
1 + 1 + 5r = 4
2 + 5r = 4
5r = 4 - 2
5r = 2
r = 2/5

p = 1/x
1/3 = 1/x
x = 3
q = 1/y
1/4 = 1/y
y = 4
r = 1/z
2/5 = 1/z
z = 5/2
Hp = { 3 , 4 , 5/2 } (D)