SOLUTION: Determine the solutions for the following systems of equations. Put your answers in ordered triple or quadruple form. 3x -4y + 6z = -7 -2x + y - 5z = -5 x + -y + z = -4 I s

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Determine the solutions for the following systems of equations. Put your answers in ordered triple or quadruple form. 3x -4y + 6z = -7 -2x + y - 5z = -5 x + -y + z = -4 I s      Log On


   

Question 1008713: Determine the solutions for the following systems of equations. Put your answers in ordered triple or quadruple form.
3x -4y + 6z = -7
-2x + y - 5z = -5
x + -y + z = -4
I solved the first one but I got huge answers and ugly fractions so I really need to know where I went wrong! I got (-59/29,-32/29,-218/29). These cannot be right!! Please help, thank you!

The second one is
x + y - z + 2w = 5
-3x + 7y -5z +4w = 13
2x -3y +2z -w = -4
x -4y +3z -3w =-9
I didn't attempt this one because I got such a strange answer for the first one I didn't want to do the whole thing only to find I did it all wrong.
Thanks again, any help is appreciated.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
No, you have a mistake somewhere.
Use Cramer's rule,
A=%28matrix%283%2C3%2C%0D%0A3%2C-4%2C6%2C%0D%0A-2%2C1%2C-5%2C%0D%0A1%2C-1%2C1%29%29
abs%28A%29=6
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A%5Bx%5D=%28matrix%283%2C3%2C%0D%0A-7%2C-4%2C6%2C%0D%0A-5%2C1%2C-5%2C%0D%0A-4%2C-1%2C1%29%29
abs%28A%5Bx%5D%29=-18
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A%5By%5D=%28matrix%283%2C3%2C%0D%0A3%2C-7%2C6%2C%0D%0A-2%2C-5%2C-5%2C%0D%0A1%2C-4%2C1%29%29
abs%28A%5By%5D%29=24
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A%5Bz%5D=%28matrix%283%2C3%2C%0D%0A3%2C-4%2C-7%2C%0D%0A-2%2C1%2C-5%2C%0D%0A1%2C-1%2C-4%29%29
abs%28A%5Bz%5D%29=18
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x=abs%28A%5Bx%5D%29%2Fabs%28A%29=%28-18%29%2F6=-3
y=abs%28A%5By%5D%29%2Fabs%28A%29=24%2F6=4
z=abs%28A%5Bz%5D%29%2Fabs%28A%29=18%2F6=3
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Do the 4x4 matrix the same way.
Repost if you get stuck.