Question

how do we do addition method with 3 equations?
4x+8y-4z=4
3x+8y+5z=-11
-2x+y+12z=-17

Answer 1

Which three equations? Write them down.

Answer 2

okay

Answer 3

4x+8y-4z=4
3x+8y+5z=-11
-2x+y+12z=-17

Answer 4

The addition method is also called the elimination method. Do you know how to do the elimination method ?

Answer 5

yes, i got up to where i got -x+4z=-15, but i dont know how to do the other steps

Answer 6

ok...I see you cancelled out the y's....let me show you...hold on...elimination methodisnot hard, just time consuming

Answer 7

okay :]

Answer 8

4x + 8y - 4z = 4 --> (-1)4x + 8y - 4z = 4
3x + 8y + 5z = -11
-----------------
-4x - 8y + 4z = -4
3x + 8y + 5z = - 11
------------------add
-x + 9z = - 15

Is this how you started....because I got something different.

Answer 9

oh yeah thats what i got , i just typed it wrong

Answer 10

now you have to take the last to equations and do the same thing....just remember, what you cancelled out in the first two equations, you have to cancel out in the last two equations. So, do the last two equations and cancel out the y's as well. Try that and tell me what you get

Answer 11

oops....the last two equations....

Answer 12

wait, i do
3x+8y+5z=-11
-2x+y+12z=-17 ?

Answer 13

okay...you have to find a way to cancel out the y's. Try multiplying the last equation by a -8.

Answer 14

okay

Answer 15

okay i got 19x-91z=-125

Answer 16

3x + 8y + 5z = -11
-2x + y + 12z = - 17 -->(-8)-2x + y + 12z = - 17
-----------------
3x + 8y + 5z = - 11
16x - 8y - 96z = 136 (result of multiplying by -8)
------------------add
19x - 91z = 125

almost....

now you take the answers you got...the two that you eliminated the y's from, add them and eliminate any one of those variables to find the other variable.
Do you understand ?

Answer 17

oh okay, so we should try to cancel out the same variables to get the two equations?

Answer 18

yes.....and now that you have the two equations, the ones where you cancelled out the y's....do the same thing with them and cancel out a variable. Do you understand or do you want me to show you ?

Answer 19

i understand , but i want to make sure i did it right

Answer 20

I will show you.....

these are the two equations you have where the y's have been cancelled out :
-x +9z = - 15 -->(19)-x + 9z = - 15
19x - 91z = 125
---------------
-19x + 171z = - 285 (result of multiplying by 19)
19x - 91z = 125
---------------add
0 + 80z = - 160
x = - 160/80
x = - 2

do you understand what I just did ?

Answer 21

isnt it 60? and z?

Answer 22

my bad....it is z....but it is not 60. How did you get 60 ?

Answer 23

wait, i messed up , i got 80 too

Answer 24

good. Now you can substitute the -2 in for z in either of the equations that the y was cancelled out of . Do you understand ?

Answer 25

yeah, so do i get x=3

Answer 26

how would i get y tho?

Answer 27

let me check...
-x +9z = -15
-x + 9(-2) = - 15
-x - 18 = - 15
-18 + 15 = x
-3 = x

or you could have done this one...
19x - 91z = 125
19x - 91(-2) = 125
19x + 182 = 125
19x = 125 - 182
19x = - 57
x = - 3

either way you will get x = - 3

do you understand this ?

Answer 28

yeah, i understand that part but what about y?

Answer 29

To get y, you just plug in your known variables into any of the three original equations and you should be able to find y.Once you know all 3 variables, you can check by subbing in all known variables into any of the original equations and if they come out equal, your answers are correct.

Answer 30

oh okay, i get it :] thank you very much!

Answer 31

you are very welcome. Be careful with elimination method because it is easy to make mistakes. And if you make a mistake at the beginning, it will travel through the rest of the problem and you won't get the right answer .

Answer 32

oh okay , yeah, i had messed up and i noticed it did mess up the problem
. :]

Answer 33

so did I....I told you x when it should have been z...lol

Answer 34

lol its okay, you helped me out a lot! thank you very much once again, i appreciate .

Answer 35

it.

Answer 36

anytime :)