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Answer 1

Verified answer

Bab Persamaan Linear
Matematika SMA Kelas X

1/(x + y) = a
1/(x + z) = b
1/(y + z) = c

1/(x + y) + 1/(y + z) = 4
a + c = 4

1/(y + z) + 1/(x + z) = 11
c + b = 11

1/(x + z) + 1/(x + y) = 3
b + a = 3

*******************************************

a + b = 3
a + c = 4
-------------- -
b - c = -1

********************************************

b + c = 11
b - c = -1
---------------- +
   2b = 10
     b = 5

b + c =11
5 + c = 11
c = 11 - 5
c = 6

a + b = 3
a + 5 = 3
a = 3 - 5
a = -2

*****************************************

1/(x + y) = a
1/(x + y) = -2
x + y = -1/2

******************************************

1/(x + z) = b
1/(x + z) = 5
x + z = 1/5

*******************************************

1/(y + z) = c
1/(y + z) = 6
y + z = 1/6

********************************************

x + z = 1/5
y + z = 1/6
----------------- -
x - y = 1/30

x + y = -1/2
x - y = 1/30
------------------ +
2x = -14/30
x = -7/30

**************************

x + y = -1/2
-7/30 + y = -1/2
y = 7/30 - 15/30
y = -8/30
y = -4/15

x + z = 1/5
-7/30 + z = 1/5
z = 7/30 + 6/30
z = 13/30

jadi, x = -7/30
       y = -4/15
       z = 13/30