Question

Tentukan himpunan penyelesaian dari

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

Answer 1

Verified answer

Misal a = 1/x , b = 1/y dan c = 1/z
maka :
2a - b + 2c = 1
3a + 2b - 3c = -8
a - 4b - c = 2

2a - b + 2c = 1 (× 2)
3a + 2b - 3c = -8 (× 1)

4a - 2b + 4c = 2
3a + 2b - 3c = -8
------------------------- +
7a + c = -6 => pers.I

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

8a - 4b + 8c = 4
...a - 4b - ...c = 2
------------------------ -
7a + 9c = 2 => pers.II


pers.I => .7a + c = -6
pers.II => 7a + 9c = 2
.................------------------ -
.........................-8c = -8
.............................c = -8/-8 = 1
7a + c = -6
7a + 1 = -6
7a = -6 - 1
7a = -7
a = -7/7 = -1

2a - b + 2c = 1
2(-1) - b + 2(1) = 1
-2 - b + 2 = 1
-b = 1
b = 1/-1 = -1

maka :
a = 1/x
-1 = 1/x
x = -1

b = 1/y
-1 = 1/y
y = -1

c = 1/z
1 = 1/z
z = 1

Jadi HPnya adalah {-1 , -1 , 1}