SOLUTION: Hello, please i need help solving this problem step by step: -4x-8y-z=-64 x+2y+7z=43 -8x+y+z=-65 Thank you

Algebra ->  Linear-equations -> SOLUTION: Hello, please i need help solving this problem step by step: -4x-8y-z=-64 x+2y+7z=43 -8x+y+z=-65 Thank you      Log On


   

Question 932411: Hello, please i need help solving this problem step by step:
-4x-8y-z=-64
x+2y+7z=43
-8x+y+z=-65
Thank you
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

-4x-8y-z=-64.....eq.1
x%2B2y%2B7z=43.....eq.2
-8x%2By%2Bz=-65.....eq.3
___________________________
start with
-4x-8y-z=-64.....eq.1
-8x%2By%2Bz=-65.....eq.3
_____________________________add both
-4x-8y-z-8x%2By%2Bz=-64-65

-12x-7y-cross%28z%29%2Bcross%28z%29=-129
-12x-7y=-129....solve for y
-12x%2B129=7y
-%2812%2F7%29x%2B129%2F7=y
-%2812%2F7%29x%2B129%2F7=y
y=-1.71x%2B18.43.........1a
go to x%2B2y%2B7z=43.....eq.2, substitute y and solve for x

x%2B2%28-1.71x%2B18.43%29%2B7z=43

x-3.42x%2B36.86%2B7z=43
-2.42x=-7z%2B43-36.86
-2.42x=-7z%2B6.14
2.42x=7z-6.14
x=7z%2F2.42-6.14%2F2.42
x=-2.89z-2.54.........1b

-4%28-2.89z-2.54%29-8%28-1.71x%2B18.43%29-z=-64.....eq.1
11.56z%2B10.16%2B13.68%28-2.89z-2.54%29-147.44-z=-64
11.56z%2B10.16-39.54z-34.75-147.44-z=-64
-28.98z-172.03=-64
-28.98z=172.03-64
-28.98z=108.03
z=108.03%2F-28.98
highlight%28z=-3.73%29
go to
x=-2.89%28-3.73%29-2.54.........1b
x=10.7797-2.54
highlight%28x=8.24%29


y=-1.71%2A8.24%2B18.43.........1a
y=-14.09%2B18.43
highlight%28y=4.34%29

-4%2A8.24-8%2A4.34-%28-3.73%29=-64.....eq.1
-32.96-34.72%2B3.73=-64
-63.95=-64...round it to whole number
-64=-64