SOLUTION: x+y+z=6 2x-y+3z=9 -x+2y+2z=9 "please show me step by step using elimination"

Question 105012: x+y+z=6
2x-y+3z=9
-x+2y+2z=9

"please show me step by step using elimination"
Answer by elima(1433) (Show Source): You can put this solution on YOUR website!
x+y+z=6
2x-y+3z=9
-x+2y+2z=9
With the elimination, you want to eliminate one of the variables;
so we will take the first equation and the second, add them together so we can eliminate the x;
x+y+z=6
-x+2y+2z=9
-----------
3y+3z=15
================
Now lets take second equation and the third and eliminate the x,to do that we need to multiply the third equation by 2;
2(-x+2y+2z=9)
-2x+4y+4z=18
========================
Now lets add the second and third equations;
2x-y+3z=9
-2x+4y+4z=18
-------------
3y+7z=27
==============
Now we can add our 2 new equations together;
3y+3z=15
3y+7z=27
==============
multiply one equation by -1 so we can eliminate a variable;
3y+3z=15
-3y-7z=-27
----------
-4z=-12
z=3
=============
Now plug that into one of the equations and solve for the y;
3y+3(3)=15
3y+9=15
3y=6
y=2
===============
Now that we have z and y, we can put those into the original equation and solve for x;
x+y+z=6
x+2+3=6
x+5=6
x=1
so answers are;
x1, y=2, z=3
I know this is long and can be tedious, but I hope you understand
:)

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