jika x,y, dan z memenuhi sistem persamaan: 1/x+2/y+2/z=10 2/x+1/y-3/z=4 1/x-3/y+4/z=-3 maka x+y+z adalah ..... ket. 1/x itu pecahan 1 per x

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

a + 2b + 2c = 10 ... (1)
2a + b - 3c = 4 ... (2)
a - 3b + 4 = -3 ... (3)

Eliminasi (a) : (1) dan (2)
2a + 4b + 4c = 20
2a + b - 3c = 4
Kurangkan
3b + 7c = 16 ... (4)

(1) dan (3)
Kurangkan
5b - 2c = 13 ... (5)

Eliminasi (b) : (4) dan (5)
15b + 35c = 80
15b - 6c = 39
Kurangkan
41c = 41
c = 1
1/z = 1
z = 1 ✔

Dr pers (4)
3b + 7c = 16
3b = 9
b = 3
1/y = 3
y = 1/3 ✔

Dr pers (3)
a - 3b + 4c = -3
a - 9 + 4 = -3
a = 2
1/x = 2
x = 1/2 ✔

••
x + y + z = 11/6 ✔

1/x +2/y + 2/z = 10
2/x +1/y - 3z = 4
1/x -3/y +4/z = -3
misal 1/x = a, 1/y = b, dan 1/z = c, maka
a + 2b + 2c = 10 ...(1)
2a + b -3 c = 4 ...(2)
a - 3b + 4c = -3 ...(3). ambil (1) dan (2), dieliminir a, maka. (1) x 2
2a + 4b + 4c = 20
2a + b - 3 c = 4
---------------------- -
3b + 7c = 16.....(4)
Ambil (1) dan (3), eliminasi a.
a + 2b + 2c = 10
a - 3 b + 4c = -3
--------------------- -
5b - 2c = 13....(5).
Ambil (4) dan (5), eliminasi b, maka
3b + 7c = 16. x 5
5b - 2c = 13. x 3
15b + 35c = 80
15b - 6c = 39
------------------ -
41c = 41
c = 41/41 = 1. Ambil (4)
3b + 7c = 16
3b + 7.1 = 16
3b + 7 = 16
3b = 16 -7
3b = 9
b = 9/3
b = 3. Ambil (1)
a + 2b + 2c = 10
A
a + 2.3 + 2.1 = 10
a + 6 + 2 = 10
a = 10-8 = 2, maka
1/x = 2.==> x = 1/2
1/y = 3 ==> y = 1/3
1/z = 1 ==> z = 1
maka x + y + z = 1/2+1/3+1
= 3/6+2/6 +6/6
= 11/6
= 1 5/6