Tentukan nilai 2x+6y+z jika diketahui sistem persamaan berikut 2/x-1/y-2/z=3 1/x+2/y+4z=4 1/x-1/y-3/z=2

jawab

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

2/x - 1/y - 2/z = 3 → 2a - b - 2c= 3 ..(i)
1/x + 2/y+  4/z = 4 → a + 2b + 4c = 4 ....(ii)
1/x + 1/y - 3/z =  2 → a  + b - 3c= 2 ....(iii)

(i dan ii)
2a - b- 2c = 3
a + 2b + 4c = 4...}kali 2

2a - b - 2c = 3
2a + 4b + 8c = 8...||(-)
-5b - 10c = - 5 atau b + 2c = 1 ....(iv)

(ii dan iii)
a+ 2b + 4c = 4
a - b - 3c = 2 ....||(-)
3b + 7c  = 2...(v)

(iv dan v)
b + 2c = 1...}kali 3
3b + 7c = 2 

3b + 6c = 3
3b + 7c = 2....||(-)
-c = 1
c = -1

b + 2c = 1...(iv)
b = 1 - 2c
b = 1 - 2(-1)
b = 3

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

a= 2 → x = 1/a = 1/2
b = 3 → y = 1/b= 1/3
c= -1→ z = 1/c = - 1
nilai  2x + 6y + z = 2(1/2) + 6(1/3) + (-1)
2x + 6y + z = 1 + 2 -1
2x + 6y + z = 2