Question

Tersedia tiga persamaan linear sebagai berikut

1/x + 2/y + 3/z = 8
2/x + 2/y + 4/z = 10
2/x + 4/y + 2/z = 4

Selesaikan persamaan linear di atas

Answer 1

Verified answer

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

a + 2b + 3c = 8 .............(persamaan 1)
2a + 2b + 4c = 10..........(persamaan 2)
2a + 4b + 2c = 4 ..........(persamaan 3)

eliminasi persamaan 1 dan 2
a + 2b + 3c = 8
2a + 2b + 4c = 10
------------------------- -
-a - c = -2
a + c = 2 ..................(persamaan 4)

eliminasi persamaan 1 dan 3
a + 2b + 3c = 8
2a + 4b + 2c = 4
------------------------
2a + 4b + 6c = 16
2a + 4b + 2c = 4
------------------------- -
4c = 12
c = 3
1/z = 3
z = 1/3

masukkan nilai c ke persamaan 4
a + c = 2
a + 3 = 2
a = -1
1/x = -1
x = -1

a + 2b + 3c = 8
-1 + 2b + 9 = 8
2b = 8 - 8
b = 0
1/y = 0
y = 1/0