SOLUTION: Im haveing troble doing this equation. I get mixed up in the steps. Can you please help? Thank you! 6x-y+2z=8 2x+3y-z=-9 4x+2y+5z=1

Algebra ->  Sequences-and-series -> SOLUTION: Im haveing troble doing this equation. I get mixed up in the steps. Can you please help? Thank you! 6x-y+2z=8 2x+3y-z=-9 4x+2y+5z=1      Log On


   

Question 995315: Im haveing troble doing this equation. I get mixed up in the steps. Can you please help? Thank you!
6x-y+2z=8
2x+3y-z=-9
4x+2y+5z=1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
6x-y%2B2z=8.....eq.1
2x%2B3y-z=-9.....eq.2
4x%2B2y%2B5z=1.....eq.3
------------------------
here you have the system of three equations with three unknown variables: x,y, and z
first, take two equations and try to eliminate one unknown variable

6x-y%2B2z=8.....eq.1
2x%2B3y-z=-9.....eq.2....both sides multiply by 2
-----------------------------
6x-y%2B2z=8.....eq.1
4x%2B6y-2z=-18.....eq.2
------------------------------add both
6x-y%2B2z%2B4x%2B6y-2z=8%2B%28-18%29
10x%2Bcross%282z%29%2B5y-cross%282z%29=8-18
10x%2B5y=-10...solve for x
10x=-5y-10
x=-5y%2F10-10%2F10
x=-y%2F2-1................eq.1a
do same with other two equations:
2x%2B3y-z=-9.....eq.2..........both sides multiply by 5
4x%2B2y%2B5z=1.....eq.3
-----------------------
10x%2B15y-5z=-45.....eq.2
4x%2B2y%2B5z=1.....eq.3
-----------------------------add
10x%2B15y-cross%285z%29%2B4x%2B2y%2Bcross%285z%29=-45%2B1
14x%2B17y=-44
14x=-17y-44
x=-17y%2F14-44%2F14
x=-%2817%2F14%29y-22%2F7 ................eq.1b
since 1a and 1b have same left sides, equal the right sides and solve for y
-y%2F2-1=-%2817%2F14%29y-22%2F7
%2817%2F14%29y-y%2F2=1-22%2F7
17y%2F14-7y%2F14=7%2F7-22%2F7
10y%2F14=-15%2F7
10y%2A7=-15%2A14
70y=-210
y=-210%2F70
highlight%28y=-3%29
go back to 1a, plug in -3 for y and solve for x
x=-y%2F2-1................eq.1a
x=-%28-3%29%2F2-1
x=3%2F2-1
x=3%2F2-2%2F2
highlight%28x=1%2F2%29

now go to any of given eq. plug in values for x and y, and solve for z
2x%2B3y-z=-9.....eq.2
2%281%2F2%29%2B3%28-3%29%2B9=z
1-cross%289%29%2Bcross%289%29=z
highlight%28z=1%29

so, your solutions are:
highlight%28x=1%2F2%29
highlight%28y=-3%29
highlight%28z=1%29