SOLUTION: Solve the system of equations. 2x+8y+z=17 -x+y+4z=-7 x+4y+4z=-2 I would appreciate the help. thank you

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the system of equations. 2x+8y+z=17 -x+y+4z=-7 x+4y+4z=-2 I would appreciate the help. thank you      Log On


   

Question 446133: Solve the system of equations.
2x+8y+z=17
-x+y+4z=-7
x+4y+4z=-2

I would appreciate the help. thank you
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
2x+8y+1 z=17--------------1
-1x+1y+4z=-7--------------2
1x+4y+4z=-2--------------3

consider equation 1 &2 Eliminate y
Multiply 1 by 1
Multiply 2 by -8
we get
2x+8y+z =17
8x-8y-32z=56
Add the two
10x-31z=73 -------------4
consider equation 2 & 3 Eliminate y
Multiply 2 by-4
Multiply 3 by 1
we get
4x-4y-16z=28
x+4y+4z=-2
Add the two
5x-12z=26 -------------5 5
Consider (4) & (5) Eliminate x
Multiply 4 by 1
Multiply (5) by -2
we get
10x-31z=73
-10x+24z=-52
Add the two
-7z=21
/ -7
z=-3
Plug the value of z in 5
5x+36=26
5x=-10
x=-2
plug value of x & z in 1
-4+8y-3 =17
8y=4+3+17
y=24
m.ananth@hotmail.ca