solving systems of equations.. help, please?

L

LocaChica16

New member
Joined
Sep 8, 2005
Messages
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Hey guys, if you could help me with this I'd appreciate it.
Basically, the problem I was given was;

2x-y=2
3z=21
4x+z=19

And I'm supposed to solve for each variable.. which I did, and I got z=7, x=-3, and y=-8... which all plug in and work correctly except for in the last equation, if I change x to positive 3 then the last equation works, but the first two don't. I'm so confused, so if anyone can show me what I'm doin wrong I'd love it! Thank you.
 
I'm sorry, but until you show your work, there is no way for us to guess where you might have made an error.

Please reply showing all of your steps, specifying the method you are supposed to be using (Cramer's Rule? matrix row operations? etc) to solve the system.

Thank you.

Eliz.
 
alright, sorry. I did it like this...

to find z I used the equation, 3z=21 which by putting that into "z" equals form I got.. z=7.

to find x, I did

2x-y=-2
2x=-1/2y-2/2
x=-1/2y-1

then I plugged the x and z values that I got into the 4x+z=19 equation,
4(-1/2y)+7=19
-2y-4+7=19
-2y+3=19
-2/-2y=16/-2
y=-8

uhm.. then I wanted to find x so I did;

2x-y=2
2x=2+y
2x=2+-8
2x/2=-6/2
x=-3

does that help??
 
LocaChica16 said:
to find x, I did

2x-y=-2
2x=-1/2y-2/2
x=-1/2y-1
Click to expand...

You're sure not very careful, LC:
your 1st post has 2x - y = 2 : why are you using 2x - y = -2 ?

2x - y = 2
2x = y + 2
x = (y + 2) / 2

now carry on...CAREFULLY!!
 
2x-y=-2 (1)
3z=21 (2)
4x+z=19 (3)

You found z from (2) perfectly.

If you wanted to find x next, then it would be a good idea to use (3), because (3) is now effectively
4x + 7 = 19

y can then be found by plugging this value of x into (1).

Is that ok?

If you would like some pointers on what you have tried:

2x-y=-2
2x=-1/2y-2/2 I think you mean x=... here. Anyway, the problem is you have subtracted y from the right-hand side, instead of adding it.
x=-1/2y-1

then I plugged the x and z values that I got into the 4x+z=19 equation,
4(-1/2y)+7=19 Another wee typo, no biggy - your next line's fine.
-2y-4+7=19
-2y+3=19
-2/-2y=16/-2 With parentheses your algebra is good here.
y=-8 Good if you hadn't made the original error.

uhm.. then I wanted to find x so I did;

2x-y=2
2x=2+y
2x=2+-8
2x/2=-6/2
x=-3 Your algebra's good again. You're just being plagued by the only mistake you made (the one at the beginning).
Click to expand...

Edit: Oh, and the mistake Denis spotted!
 
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