SOLUTION: 1/x + 2/y - 4/z = 1 2/x + 3/y + 8/z = 0 -1/x + 9/y + 10/z = 5 then solve x, y and z values.

Algebra ->  Matrices-and-determiminant -> SOLUTION: 1/x + 2/y - 4/z = 1 2/x + 3/y + 8/z = 0 -1/x + 9/y + 10/z = 5 then solve x, y and z values.      Log On


   

Question 831765: 1/x + 2/y - 4/z = 1
2/x + 3/y + 8/z = 0
-1/x + 9/y + 10/z = 5
then solve x, y and z values.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let u=1%2Fx,v=1%2Fy,w=1%2Fz
.
.
.
1.u%2B2v-4w=1
2.2u%2B3v%2B8w=0
3.-u%2B9v%2B10w=5
Use Gaussian elimination.
Multiply eq. 1 by 2 and subtract from eq. 2.
2u%2B4v-8w-2u-3v-8w=2
4.v-16w=2
Add eq. 1 and eq. 3,
u%2B2v-4w-u%2B9v%2B10w=1%2B5
5.11v%2B6w=6
Now multiply eq. 4 by 11 and subtract from eq. 5,
11v-176w-11v-6w=22-6
-182w=16
w=-16%2F182
w=-8%2F91
Now back substitute,
v-16w=2
v-16%28-8%2F91%29=2
v%2B128%2F91=182%2F91
v=54%2F91
And finally,
u%2B2v-4w=1
u%2B2%2854%2F91%29-4%28-8%2F91%29=1
u%2B108%2F91%2B32%2F91=91%2F91
u%2B140%2F91=91%2F91
u=-49%2F91
u=-7%2F13
Last step,
u=1%2Fx=-7%2F13
highlight%28x=-13%2F7%29
v=1%2Fy=54%2F91
highlight%28y=91%2F54%29
w=1%2Fz=-8%2F91
highlight%28z=-91%2F8%29