Question

8/x - 2/y + 6/z =4
2/x + 1/y+3/z =3
4/x +2/y-12/z =0

Answer 1

Verified answer

SPLTV
Kelas X

Misal 1/x = a , 1/y = b , 1/z = c

Maka
8a - 2b + 6c = 4 ... (i)
2a + b + 3c = 3 ... (ii)
4a + 2b - 12c = 0 ... (iii)

Tinjau persamaan (i)

8a - 2b + 6c = 4 [÷ 2]
4a - b + 3c = 2 , b = 4a + 3c - 2 ... (iv)

Subtitusi (iv) ke persamaan (ii)

2a + 4a + 3c - 2 + 3c = 3
6a + 6c = 5 ... (v)

Subtitusi (iv) ke persamaan (iii)
4a + 2(4a + 3c - 2) - 12c = 0
4a + 8a + 6c - 4 - 12c = 0
12a - 6c = 4 ... (v)

Eliminasi (iv) dan (v)

12a - 6c = 4
6a + 6c = 5
–––––––– (+)
18a = 9
a = ½
1/x = ½
x = 2

6(½) + 6c = 5
6c = 5 - 3
6c = 2
c = ⅓
1/z = ⅓
z = 3

b = 4(½) + 3(⅓) - 2
b = 1
1/y = 1
y = 1

HP : {(2 , 1 , 3)}