Question

Soal Try-Out SBMPTN oleh ITB + LBB NF mat saintek
no 13 ... ?

Answer 1

N.B. : saya gak pakai latex ya, bu.

3/x + 3/y + 5/z = 9
kalikan dengan xyz
3yz + 3xz + 5xy = 9xyz

3/x + 2/y + 1/z = 5
kalikan dengan xyz
3yz + 2xz + xy = 5xyz

1/x + 2/y + 4/z = 7
kalikan dengan xyz
yz + 2xz + 4xy = 7xyz

sehingga didapatkan :

3yz + 3xz + 5xy = 9xyz
3yz + 2xz + xy = 5xyz
yz + 2xz + 4xy = 7xyz

eliminasi :
3yz + 3xz + 5xy = 9xyz
3yz + 2xz + xy = 5xyz
___________________ -
xz + 4xy = 4xyz
xz = 4xyz - 4xy

3yz + 2xz + xy = 5xyz
yz + 2xz + 4xy = 7xyz |x3

3yz + 2xz + xy = 5xyz
3yz + 6xz + 12xy = 21xyz
____________________ -
-4xz - 11xy = -16xyz

-4xz - 11xy = -16xyz
-4(4xyz - 4xy) - 11xy = -16xyz
-16xyz + 16xy - 11xy = -16xyz
5xy = 0
xy = 0

-4xz - 11xy = -16xyz
-4xz = -16xyz
xz = 4xyz

yz + 2xz + 4xy = 7xyz
yz + 2(4xyz) = 7xyz
yz = -xyz

jadi,
xy = 0
xz = 4xyz
yz = -xyz

3xy + 4xz + 7yz = 0 + 4(4xyz) + 7(-xyz)
= 9xyz