complete the ordered triple
8x-y+z=32
3x+2y-3z=36
x-3y+2z=-14

- anonymous

complete the ordered triple
8x-y+z=32
3x+2y-3z=36
x-3y+2z=-14

- schrodinger

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- amistre64

piece o cake... :)

- amistre64

how you wanna solve it?

- anonymous

i thought so too but when i worked the equation the way i was explained didnt get the right answer

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## More answers

- anonymous

directions say to number equations 1-3
multiply (1) by 2

- amistre64

8x - y + z =32(-3/8) 8x - y + z =32(-1/8)
3x +2y -3z =36 x -3y +2z =-14

- anonymous

what is that? confusing me more

- amistre64

We are multiplying row 1 by a number that will turn the first term into a negative of the equation underneath it.
-3x +3/8 y -3/8z = -96/8 -1x +1/8 y -1/8z = -32/8
3x + 2y -3 z = 36 x -3 y +2 z =-14
--------------------- --------------------

- amistre64

-3x + 3/8 y -3/8z = -12 -1x +1/8 y - 1/8z = - 4
3x +16/8y -24/8z = 36 x -24/8 y +16/8z =-14
--------------------- ----------------------
0 +19/8y -27/8z = 24 0 -23/8y +15/8z = -28
and we end up with two equations of two variables that are easier to work with....

- anonymous

the way professor taught me is multiply equation (1) by 2
16x-2y+2z=64
+3x=2y-3z=36 equation (2)
=19x-z=100 which becomes equation (4)

- amistre64

your professor choose to eliminate the "y" variable; I simply choose to start at the front and aliminatte the "x" variable. Same rules, different variable.

- anonymous

ok his way seems less confusing

- amistre64

his way keeps the fractions out :) but the process is the same.
we use the "modified" equation to eliminate a variable from the other 2

- anonymous

oh good i hate fractions

- amistre64

once you know the process..... the way you get to it is up to you :)

- amistre64

there is no special rule about : you have to use equation 1 and multiply by a certain variable yadayadayada.... pick your poison and drink ;)

- anonymous

good way to put it

- anonymous

can we work on a different one

- amistre64

we can :)

- anonymous

x+y+z=4
2x+4y+2z=4
-x+8y-3z=-34
please leave out the fractions on my end anyway

- amistre64

:) lets use equation 1 since it looks the plainest and use it to "calibrate" the other 2. ok?

- amistre64

x + y + z =4 <- what should we mulitply this bu to get rid
2x+4y+2z =4 of a variable in the bottom equation?
-------------

- amistre64

we want either a: -2x, or a -4y; or even a -2z... what variable you wanna destroy?

- amistre64

x y or z.... just pick one so we can move ahead ;)

- anonymous

x

- amistre64

good, we will destroy the "x" :)

- amistre64

the top has an "x" and the bottom has an "2x.
___ x + 2x = 0..... what do we need to fill in the blank here?

- anonymous

your doing it the hard way

- amistre64

lol..... no I aint :)

- anonymous

1

- anonymous

sry 2

- amistre64

so you want me to believe that:
1x + 2x = 0?

- amistre64

2x + 2x = 0?

- anonymous

-2

- amistre64

yay!!.... we hav a winner ;) -2 it is.

- amistre64

x + y + z =4 <- multiply everything in this top by (-2)
2x+4y+2z =4 to get
-2x -2y -2z =-8
2x +4y +2z =4 ; now add them together.
-----------------
0 +2y +0 = -4 ; wow, 2 variables with one shot lol

- anonymous

question? y do we put - between 2y, and 2z

- anonymous

because we multiply by -2, tina duh

- amistre64

i dont understand the question... yeah, thats the ticket :)

- amistre64

so we get; 2y = -4; what does y equal since its all alone?

- anonymous

better question why do we multiply by -2

- amistre64

becasue you decided to destroy the x variables...... and that meant that we needed to have a number such that:
___x + 2x = 0 ; zero means they are eliminated, destroyed, kaput right?

- anonymous

ok got it

- amistre64

(__)x + 2x = 0 ; you recall that :)

- amistre64

you sophies choiced it lol

- anonymous

going for bs in accounting didnt know this kind of math would be part of it

- anonymous

im actually a freshman

- amistre64

gotta know algebra... and thats all this is :)

- anonymous

still trying to figure out how i made it out of hs

- amistre64

So, to move ahead... we came to the conclusion that both those variables vanished in the process, and we are left with 2y=-4; whats y have to be?

- anonymous

-2

- amistre64

good, write that down someplace...y = -2 its one of your answers :)

- amistre64

Now we use equation (1) that you gave me and use it to eliminate "x" in the last one right?
x + y + z = 4
-x +8y -3z =-34

- amistre64

Is there anything we have to do to this to get:
x - x = 0?

- anonymous

do we multiply equation 1by -3?

- anonymous

1-1=0

- amistre64

no..... you chose "x" variable for elimination...stick with it to the end :)

- anonymous

ok, carry on then

- amistre64

(__)x -x = 0 ; what do we have to do to make this right? what number
do we need to use?

- amistre64

that format lied to me lol

- anonymous

? idk x represents 1 right?

- amistre64

x represents x.... 1 represents 1..... but what you a really asking is:
isnt there an invisible 1 in front of those? and I say , yes. and so you say, then the number we need is 1; and I say correct :)

- anonymous

yeah thats exactly what i was thinking

- amistre64

then we can multiply everything in the top by (1)...which seems pretty pointless right? but thats what we do :)
x + y + z =4 <-- multiply it all by (1) and we get.
-x +8y -3z =-34
x+ y+ z =4
-x+8y-3z=-34 <-- add em up
---------------
0 +7y -2z = -30

- amistre64

ummm 8 + 1 = 9 :) I forgot how to add :)

- amistre64

8y -2z = -30 now we can use this equation for some good :)

- anonymous

i got 9y-2z=-30

- amistre64

.........so did I but my fingers aint cooperating with me brain :)

- amistre64

im gonna have to hold them under the iron to teach them a lesson....

- anonymous

LOL, 8y+y would be 9y right?

- amistre64

Yes, I agree........but that pinky finger is revolting ;)

- anonymous

ok so next step is?

- amistre64

well, since we already determined a solid value for "y"...lets use it ....wiat for it........NOW!!

- amistre64

8(-2) -2z = -30
-16 - 2z = -30
-2z = -14
z = -14/-2 = 7
z = 7 yay!! write that down after you check me work..

- anonymous

we subtract -16 from both sides

- amistre64

why would we do that?
-16-16 -2z = -30-16 is true, but it gets us nowhere fast.
if we "add" 16 to both sides we get:
-16+16 -2z = -30+16

- anonymous

i got z=7

- amistre64

me too :)

- amistre64

y = -2, z = 7 lets use these in any of the others equations, but equation 1 seems lonely and wants some attention...so we will use it :)
x + y + z = 4
x +-2 + 7 = 4
x + 5 = 4
x = 4-5
x = -1; y=-2; z=7 is the solution to our equations.

- amistre64

you agree? we can double check by using these values in all the equations and seeing if the results are true...

- anonymous

i agree

- amistre64

its alot of mechanicl work, but once you know the underlying principles; the rest is just drudging thru the motions..

- anonymous

something isnt right

- anonymous

my school using mathlab and it says the answer is wrong
x,y,z
-1,-2,7

- anonymous

it was 9y instead of 8y thats y i kept getting confused

- amistre64

x+y+z=4 <- we know this ones good.... we used it to find x
......................................
2(-1)+4(-2)+2(7)=4
-2 -8 +14 = 4
-10 + 14 = 4
4 = 4 ..... its good there
........................................
-(-1)+8(-2)-3(7)=-34
1 -16 -21 = -34
-14-21 = -34
-35 = -34 is off.....

- anonymous

the equation is -x+8y-3z=-34
but when we added that to x+y+z=4
we got 0+8y-2z=-30
it should have been 0+9y-2z=-30

- amistre64

1-16 = -15......

- amistre64

you telling me you gave me the wrong equations?

- amistre64

9y-2z=-30...and we used 8y right? lol

- amistre64

this is soooo much easier to keep track of on paper, i gotta tell ya :)

- anonymous

no the equations were right the math was wrong your fingers really screwed it up but just by one number the answer is
x,y,z
-1,-2,6

- anonymous

add an extra 5mins on that iron

- amistre64

lol.... gonna buy me one of those cigar cutters..... see what they think o that :)

- anonymous

lmao, so what are you majoring in

- amistre64

major in math hopefully; and minor in business

- anonymous

no wonder i just thought you were a genius with math

- amistre64

nah....just a normal genuis ;)

- amistre64

gonna take calculus 1 and stats durig the summer if the classes dont cancel

- amistre64

already taught myself alot up to calculus3....stats im rusty on

- anonymous

i hope this is all the math i have to take,
WOW! i sure am glad i found you you most likely just saved this quarter for me I was crying the other night because i sucked so bad.

- amistre64

well, I cant teach you everything in one shot :) but most of algebra you already learned..and thats all this is

- amistre64

you just need to be able to see that you know it :)

- anonymous

i took a few years off between hs and college, and i barely passed it

- amistre64

hs dont count, thats for kids anyways ;)

- amistre64

my daughter doesnt like me to help her with her homework because what she really wants is someone to just hand her the answers ...

- anonymous

my son too hes 9

- amistre64

becoming disciplined and focused is the key...nd most kids aint acquired that skill :)

- anonymous

i know a few adults that havent either , i guess it really boils down to how bad you want to succeed

- anonymous

8.3-y=-5.6

- amistre64

y = 13.9 is my guess

- anonymous

can i give you another equation and this time instead of helping me u just ck my answer, if you have nothing else to do

- amistre64

I can try :)

- anonymous

x+y+z=4
2x+4y+2z=4
-x+8y-3z=-34

- amistre64

we just did that one :)

- anonymous

yep sry gave you the wrong one
x+y+z=5
2x+5y+2z=13
-x=9y-3z=-3

- amistre64

i got it already...did it on paper :)

- anonymous

ok gonna have to give me a min,

- amistre64

use the force luke...the force!!

- anonymous

x,y,z
3,1,1

- amistre64

close...but no ;)

- anonymous

is the z=-1

- amistre64

answers are:
(x,y,z)
(0,1,4)

- anonymous

nowhere near close

- amistre64

lol....

- anonymous

ok what did i do wrong

- amistre64

i dont know, my mind reading skills are a little lacking

- anonymous

oh thought that was part of being a genious

- amistre64

x+y+z=5 (-2)
2x+5y+2z=13
-2x-2y-2z=-10
2x+5y+2z=13
----------------
0 +3y + 0 = 3 ; y = 1
.............................................

- amistre64

I said genius not circus freak ;)

- anonymous

got that part right

- amistre64

x+y+z=5 (1)
-x+9y-3z=-3
x+y+z=5
-x+9y-3z=-3
--------------
0 +10y -2z = 2 ; since y = 1, use it here
..............................................................
10(1) -2z = 2
10 -2z = 2
-2z = -8
z = 4
....................................

- amistre64

x+y+z = 5
x + 1 + 4 = 5
x + 5 = 5
x = 5-5
x = 0

- amistre64

your thinking: Damn!! I was thisssss close :)

- anonymous

i forgot to subtract 10 from both sides 2-10 =-8

- amistre64

aha!! that sly and coy, and other adjectivial words meaning roughly the same thing, little bugger

- anonymous

ok i will let you get to ur work and i will work on the rest by myself r u gonna b around in case i need help?

- amistre64

if I am. ill be the one with the tights and the cape ;) and the "M" on my chest..

- anonymous

great not sure what i could help u with but let me know,

- amistre64

..... k :)

- anonymous

Superhero hunh. lolz!!!

- anonymous

hey amistre64 u there

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