SOLUTION: solve step by step to solve linear equation with 3 variables, can you help me solve this step by step please? 2x-4y-z=17 x+2y-z=0 4x-y-z=6

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: solve step by step to solve linear equation with 3 variables, can you help me solve this step by step please? 2x-4y-z=17 x+2y-z=0 4x-y-z=6      Log On


   

Question 753656: solve step by step to solve linear equation with 3 variables, can you help me solve this step by step please?
2x-4y-z=17
x+2y-z=0
4x-y-z=6
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2x-4y-z=17...eq.1
x%2B2y-z=0...eq.2
4x-y-z=6...eq.3
_________________________
x%2B2y-z=0...eq.2..solve for x

x=z-2y...eq.2a.......substitute in .eq.1

2%28z-2y%29-4y-z=17...eq.1
2z-4y-4y-z=17
z-8y=17....solve for z
z=17%2B8y....eq.1a
go to x=z-2y...eq.2a and substitute z
x=17%2B8y-2y
x=17%2B6y........eq.2b
go to 4x-y-z=6...eq.3 and substitute z from eq.1a and x from eq.2b
4%2817%2B6y%29-y-%2817%2B8y%29=6.....solve for y
68%2B24y-y-17-8y=6
51%2B24y-9y=6
15y=6-51
15y=-45
y=-45%2F15
highlight%28y=-3%29
go back to x=17%2B6y........eq.2b and find x
x=17%2B6%2A%28-3%29
x=17-18
highlight%28x=-1%29
go back to z=17%2B8y....eq.1a and find z
z=17%2B8%28-3%29
z=17%2B-24
highlight%28z=-7%29

check:
x%2B2y-z=0...eq.2..plug in highlight%28x=-1%29,highlight%28y=-3%29, and highlight%28z=-7%29
-1%2B2%28-3%29-%28-7%29=0
-1-6%2B7=0
-7%2B7=0
0=0 which confirms our solutions