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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
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3y+3z=15
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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
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Now lets add the second and third equations;
2x-y+3z=9
-2x+4y+4z=18
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3y+7z=27
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Now we can add our 2 new equations together;
3y+3z=15
3y+7z=27
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multiply one equation by -1 so we can eliminate a variable;
3y+3z=15
-3y-7z=-27
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-4z=-12
z=3
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Now plug that into one of the equations and solve for the y;
3y+3(3)=15
3y+9=15
3y=6
y=2
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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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