Question

Jika x,y,dan z adalah penyelesaian sistem persamaman x+y/2=10 dan y/4-z=-2 dan z/2+x/3=4 maka nilai x+y+z adalah?

Answer 1

Verified answer

Bab Persamaan Linear Tiga Variabel
Matematika SMA Kelas X

x + y/2 = 10 → dikali 2, menjadi 2x + y = 20
y/4 - z = -2 → dikali 4, menjadi y - 4z = -8
z/2 + x/3 = 4→ dikali 6, menjadi 3z + 2x = 24

y + 2x = 20
y - 4z = -8
----------------- -
2x + 4z = 28
2x + 3z = 24
------------------ -
z = 4

y - 4z = -8
y = -8 + 4 . 4
y = 8

y + 2x = 20
8 + 2x = 20
2x = 20 - 8
x = 12/2
x = 6

x + y + z = 6 + 8 + 4 = 18

Answer 2

Verified answer

Diketahui :
x + y/2 = 10
y/4 - z = -2
z/2 + x/3 = 4

Ditanya : nilai x + y + z ?

Dijawab :
x + y/2 = 10
(2x + y) / 2 = 10
2x + y = 20..............(pers.1)

y/4 - z = -2
(y - 4z) / 4 = -2
y - 4z = -8.................(pers.2)

z/2 + x/3 = 4
(3z + 2x) / 6 = 4
3z + 2x = 24...........(pers.3)

Kita ubah pers.2 menjadi :
y - 4z = -8
y = 4z - 8

Masukkan y = 4z - 8 ke pers.1
2x + y = 20
2x + (4z - 8) = 20
2x + 4z = 28..........(pers.4)

Eliminasi pers.3 dan 4
2x + 3z = 24
2x + 4z = 28
_________ _
- z = - 4
z = -4 / (-1)
z = 4

Masukkan z = 4 ke pers.2
y - 4z = - 8
y - 4 (4) = -8
y - 16 = -8
y = -8 + 16
y = 8

Masukkan y = 8 ke pers.1
2x + y = 20
2x + 8 = 20
2x = 20 - 8
2x = 12
x = 12/2
x = 6

HP : {x, y, z} = {6, 8, 4}

Nilai x + y + z
= 6 + 8 + 4
= 14 + 4
= 18

Jadi, nilai x + y + z adalah 18