Question

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

Answer 1

piece o cake... :)

Answer 2

how you wanna solve it?

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

what is that? confusing me more

Answer 7

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
--------------------- --------------------

Answer 8

-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....

Answer 9

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)

Answer 10

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.

Answer 11

ok his way seems less confusing

Answer 12

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

Answer 13

oh good i hate fractions

Answer 14

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

Answer 15

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

Answer 16

good way to put it

Answer 17

can we work on a different one

Answer 18

we can :)

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

x

Answer 25

good, we will destroy the "x" :)

Answer 26

the top has an "x" and the bottom has an "2x.

___ x + 2x = 0..... what do we need to fill in the blank here?

Answer 27

your doing it the hard way

Answer 28

lol..... no I aint :)

Answer 29

1

Answer 30

sry 2

Answer 31

so you want me to believe that:

1x + 2x = 0?

Answer 32

2x + 2x = 0?

Answer 33

-2

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

because we multiply by -2, tina duh

Answer 38

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

Answer 39

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

Answer 40

better question why do we multiply by -2

Answer 41

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?

Answer 42

ok got it

Answer 43

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

Answer 44

you sophies choiced it lol

Answer 45

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

Answer 46

im actually a freshman

Answer 47

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

Answer 48

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

Answer 49

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?

Answer 50

-2

Answer 51

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

Answer 52

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

Answer 53

Is there anything we have to do to this to get:

x - x = 0?

Answer 54

do we multiply equation 1by -3?

Answer 55

1-1=0

Answer 56

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

Answer 57

ok, carry on then

Answer 58

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

Answer 59

that format lied to me lol

Answer 60

? idk x represents 1 right?

Answer 61

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 :)

Answer 62

yeah thats exactly what i was thinking

Answer 63

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

Answer 64

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

Answer 65

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

Answer 66

i got 9y-2z=-30

Answer 67

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

Answer 68

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

Answer 69

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

Answer 70

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

Answer 71

ok so next step is?

Answer 72

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

Answer 73

8(-2) -2z = -30

-16 - 2z = -30

-2z = -14

z = -14/-2 = 7

z = 7 yay!! write that down after you check me work..

Answer 74

we subtract -16 from both sides

Answer 75

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

Answer 76

i got z=7

Answer 77

me too :)

Answer 78

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.

Answer 79

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

Answer 80

i agree

Answer 81

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

Answer 82

something isnt right

Answer 83

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

Answer 84

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

Answer 85

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.....

Answer 86

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

Answer 87

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

Answer 88

you telling me you gave me the wrong equations?

Answer 89

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

Answer 90

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

Answer 91

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

Answer 92

add an extra 5mins on that iron

Answer 93

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

Answer 94

lmao, so what are you majoring in

Answer 95

major in math hopefully; and minor in business

Answer 96

no wonder i just thought you were a genius with math

Answer 97

nah....just a normal genuis ;)

Answer 98

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