1/a + 1/d=1/4 1/d + 1/t =1/3 1/a + 1/t =1/2,4 ini pakai sistem spltv

Bab Persamaan Linear
Matematika SMA Kelas X

1/a = p
1/d = q
1/t = r

1/a + 1/d = 1/4
p + q = 1/4

1/d + 1/t = 1/3
q + r = 1/3

1/a + 1/t = 1/2,4
p + r = 1 : (24/10)
p + r = 10/24
p + r = 5/12

p + r = 5/12
q + r = 1/3
----------------- -
p - q = 5/12 - 1/3
p - q = 5/12 - 4/12
p - q = 1/12

p + q = 1/4
p - q = 1/12
----------------- +
2p = 1/4 + 1/12
2p = 3/12 + 1/12
2p = 4/12
2p = 1/3
p = 1/6

p - q = 1/12
1/6 - q = 1/12
q = 1/6 - 1/12
q = 2/12 - 1/12
q = 1/12

p + r = 5/12
1/6 + r = 5/12
r = 5/12 - 1/6
r = 5/12 - 2/12
r = 3/12
r = 1/4

1/a = p
1/a = 1/6
a = 6

1/d = q
1/d = 1/12
d = 12

1/t = r
1/t = 1/4
t = 4

jadi, a = 6; d = 12; t = 4

1/a + 1/d = 1/4
1/d + 1/t = 1/3
1/a + 1/t = 1/2,4 = 5/12
Jumlah kan
2(1/a + 1/d + 1/t) = 1
1/a + 1/d + 1/t = 1/2

•
1/a + 1/d = 1/4
1/2 - 1/t = 1/4
1/t = 1/4
t = 4

••
1/d + 1/t = 1/3
1/2 - 1/a = 1/3
1/a = 1/6
a = 6

•••
1/a + 1/t = 5/12
1/2 - 1/d = 5/12
1/d = 1/12
d = 12

Jawab :
(a, d, t,) = (6, 12, 4)