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November 19th, 2011, 07:31 PM   #1
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system of equations (find x,y,z) questions

Hi. I have problem with these two questions.

1.
3x+2y-z=-2
4x-5y+2z=1
7x+y-2z=-3

So I did use 1st and 2nd equation to get 10x-y=-3 and 1st and 3rd to get -x+3y=-1. If I use these two equations I get y=-7/31 and when I plug this in I get x=-10/31. Now I plug those two for x and y on 1st equation I get z=18/31. So solution set for this equation comes out (-7/31,-10/31,18/31) for x,y,z order. When I plug these 3 #s for x,y,z for 1st and 2nd equations I get -2 and 1 which is correct answer. The problem is when I plug them in 3rd equation, I don't get -3 but I get -3.64.... is my answer wrong or did I make some mistake? plz help.


Here is 2nd problem I am having trouble with. I'm supposed to find x, y, z and z is arbitrary #

2.
5x-y+3z=-7
2x+4y+9z=11

So if z is arbitrary, I solve for y, I get y=(-39z/22)+(69/22). If I plug that in y section, I get x=(-21z/22)-(17/22). So my answer set is ( (-21z/22)-(17/22), (-39z/22)+(69/22), z(arbitrary) ).
Is this right answer? I need help.
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November 19th, 2011, 07:56 PM   #2
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Re: system of equations (find x,y,z) questions

Quote:
Originally Posted by shin777
3x+2y-z=-2
4x-5y+2z=1
7x+y-2z=-3
so I did use 1st and 2nd equation to get 10x-y=-3 and 1st and 3rd to get -x+3y=-1.
If I use these two equations I get y=-7/31
Noooooooo...these 2 equations will give y = -13/29

Did you not notice a shortcut: adding equations 2 and 3 right away?
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November 19th, 2011, 08:04 PM   #3
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Re: system of equations (find x,y,z) questions

Quote:
Originally Posted by shin777
Here is 2nd problem I am having trouble with. I'm supposed to find x, y, z and z is arbitrary #
5x-y+3z=-7
2x+4y+9z=11
So if z is arbitrary, I solve for y, I get y=(-39z/22)+(69/22). if I plug that in y section, I get x=(-21z/22)-(17/22). So my answer set is ( (-21z/22)-(17/22), (-39z/22)+(69/22), z(arbitrary) ).
Is this right answer? I need help.
Looks correct to me; clearer to show this way: x = (-21z - 17) / 22 and y = (-39z + 69) / 22
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November 19th, 2011, 08:18 PM   #4
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Re: system of equations (find x,y,z) questions

Ok. thx. I got first one's correct answer ( (-10/29), (-13/29), (2/29) )
I get correct answer with these x,y,z #s.

As for second one, are you sure I am right? These #s just don't look pretty enough to me to be an answer. I remember my instructor saying, I won't get pretty # answers like I did in algebra 1, 2 since this is college algebra but even so, it looks ugly.
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November 20th, 2011, 12:06 AM   #5
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The answers for the second problem may be inelegant, but they are correct.
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