diketahui sistem persamaan linear 3x-y+z=10 2x+3y-z=8 x+y-2z=-10 nilai (1/x+1/y+1/z) a.1/8 b.1/4 c.5/8 d.3/4 e.7/8

3x - y + z = 10
2x + 3y - z = 8
----------------------(+)
5x + 2y = 18 ... pers 1

3x - y + z = 10 |×2
x + y - 2z = - 10
maka
6x - 2y + 2z = 20
x + y - 2z = - 10
-------------------------(+)
7x - y = 10 ... pers 2

pers 1 & 2
5x + 2y = 18
7x - y = 10 |×2
maka
5x + 2y = 18
14x - 2y = 20
--------------------(+)
19x = 38
x = 2

subtitusi
5x + 2y = 18
5(2) + 2y = 18
10 + 2y = 18
2y = 18 - 10
2y = 8
y = 4

subtitusi
3x - y + z = 10
3(2) - 4 + z = 10
6 - 4 + z = 10
2 + z = 10
z = 10 - 2
z = 8

nilai 1/x + 1/y + 1/z
= 1/2 + 1/4 + 1/8
= 4/8 + 2/8 + 1/8
= 7/8 ( E )