Question

Solve the given linear system.
2x-y-z=5
x+y+z=7
3x-2y-3z=1

Answer 1

do you want to substitute a certain variable for this if not i'll just use z

Answer 2

i need to find all.. x,y and z

Answer 3

just for substitution purposes
from the 2nd equation you can get z=7-x-y so you can substitute this into the othe two equations to make them two variable equations to then use the elimination method on those two for 1 variable

Answer 4

so the other two become
2x-y-(7-x-y)=5/2x-y-7+x+=5/3x-7=5/3x=12
3x-2y-3(7-x-y)=1/3x-2y-21+3x+3y=1/6x+y-21=1/6x+y=22

Answer 5

luckily the first only already has the y removed so you can solve for x which is x=4

Answer 6

substitute x into the 2nd equation and solve
6(4)+y=22
24+y=22
y=-2

Answer 7

then plug x and y into the final equation
x+y+z=7
4-2+z=7
z+2=7
z=5

Answer 8

so x=4 y=-2 and z=5

Answer 9

woah...
x+y+z=7
4-2+z=7
z+2=7 <-- why did the 2 become positive?
z=5

Answer 10

4-2=2

Answer 11

it could have also been written as 2+x=7

Answer 12

ohh.. i see..

Answer 13

sorry 2+z=7

Answer 14

2x-y-(7-x-y)=5/2x-y-7+x+=5/3x-7=5/3x=12 3x-2y-3(7-x-y)=1/3x-2y-21+3x+3y=1/6x+y-21=1/6x+y=22 i dont understand this part

Answer 15

i was just showing how to simplify it and seperated it by/

Answer 16

i probably should have explained that sorry i didnt want to have to go line by line too take up so much space

Answer 17

oh.. its ok.. :)

Answer 18

still sorry for the confusion do you get it now?

Answer 19

uhm..

Answer 20

i remember having a tough time with system equations so don't worry it gets easier

Answer 21

can you show me how did you find z=7.

Answer 22

i plugged in the variables found earlier into the middle equation where we got z in the beginning

Answer 23

2x-y-z=5
x+y+z=7 <----- this one
3x-2y-3z=1

Answer 24

you could have also plugged them into the expression we used to replace z
z=7-x-y and still get the same answer
z=7-4-(-2)
z=7-4+2
z=5

Answer 25

oohh.. so z could be oth 7 &5?

Answer 26

im sorry what are you asking?

Answer 27

z can be z=7 or z= 5?

Answer 28

z is 5 the 7 just came from the equation

Answer 29

you can double check by inserting all the variables into to the equations and see if they agree with what the equations say

Answer 30

if you used 7 it wouldn't have worked

Answer 31

hmm..

Answer 32

do you sort of understand the concept?

Answer 33

kinda.. because im really slow in english..

Answer 34

ah that okay
lucky math is only letters

Answer 35

do you know that while you were explaining, i was imagining you were some sort of anime xDD

Answer 36

lolz not really but I do in fact like anime and manga

Answer 37

:3 SAO

Answer 38

hahaha yes

Answer 39

uhm.. could you answer this?
5x+10y=70
5x+25z=270
10y+25z=300.

Answer 40

lets get 10y from the first equation so 10y=70-5x you dont need to divide by 10 since the 3rd equation has 10y so you can just directly substitute like this
70-5x+25z=300
-5x+25x=230

Answer 41

whoops -5x+25z=230
then use elimination of that equation and the 2nd
5x+25z=270
-5x+25z=230
50z=500
z=10

Answer 42

then you can plug in z into the original 2nd and 3rd equations to find x and y

Answer 43

where did 5x go?

Answer 44

5x+25z=270
-5x+25z=230 <--- the first 5x got subtracted by the 5x here

Answer 45

so it got cancelled

Answer 46

for the rest of the variables
5x+25z=270
5x+25(10)=270
5x+250=270
5x=20
x=4
10y+25z=300
10y+25(10)=300
10y+250=300
10y=50
y=5

Answer 47

so
x=4 y=5 and z=10

Answer 48

what did you eat that you can answer this kind of equation xD

Answer 49

ironic considering I haven't eaten today

Answer 50

:O why?

Answer 51

its 12:30am

Answer 52

how did you get this -5x+25z=230

Answer 53

perhaps you go to sleep..

Answer 54

ets get 10y from the first equation so 10y=70-5x you dont need to divide by 10 since the 3rd equation has 10y so you can just directly substitute like this
70-5x+25z=300
-5x+25x=230

Answer 55

yeah I probably should... but i'll finish this first

Answer 56

from the substitution of y

Answer 57

oh.. yea.. thanks :DD you can go to sleep now.. i'll just go through this.. :) thanks man.

Answer 58

no problem! good luck!

Answer 59

are you a man? 'cause im not sure :)

Answer 60

Actually I am female

Answer 61

well.. that goes for a sis x)) thanks.. and Im a femae too.. thanks you very much.. arigatou

Answer 62

oyasumi! :)