Question

Solve the system by using elimination.

Answer 1

1. Add equations 1 and 3
2. Add equations 2 and 3
3. You will now have two equations with only y and z
4. Solve that system

Answer 2

okay one sec

Answer 3

okay so far i have 7y+10z=7
@Mertsj

Answer 4

So now add 2 and 3

Answer 5

i did i got 5y+6z+5 and 2y+4z=2 i added them together to get that answer

Answer 6

Add equations 1 and 3 to get 5y+6z = 5

Add equations 2 and 3 to get 2y+4z = 2

Answer 7

so it looks like you got it

Answer 8

you now have this smaller system

5y+6z = 5
2y+4z = 2

Answer 9

let's say we want to eliminate z, we would multiply the top equation by 2 and the bottom equation by -3 to get

2(5y+6z) = 2*5
-3(2y+4z) = -3*2


10y+12z = 10
-6y-12z = -6

Answer 10

notice how there's a +12z and a -12z, they would add to 0z or just 0 (and it would cancel and go away)

Answer 11

so then would we do the same for y

Answer 12

from here, just add the equations

Answer 13

10y+12z = 10
-6y-12z = -6
-------------
4y +0z = 4

4y = 4

y = ??

Answer 14

oh okay so 1

Answer 15

so each step of elimination eliminates one variable (first you eliminated x, then you eliminated z)

Answer 16

yes

y = 1

Answer 17

so

10y + 12z = 10

10(1) + 12z = 10

10 + 12z = 10

...

z = ??

Answer 18

and you probably see from here how to find x (given y and z)

Answer 19

yes thank you!!! could you pretty please help with one more??

Answer 20

ok just one more

Answer 21

k, we have to solve with substiution give me a sec and i'll have the pic

Answer 22

solve for either x or z in the last equation

Answer 23

so we add -x nd 2x to get rid of x ?

Answer 24

idk what you mean

Answer 25

in the third equation, do you want to solve for x or z?

Answer 26

z?

Answer 27

ok so what do you get when you isolate z in the third equation

Answer 28

2x+2=4?

Answer 29

2x + 2z = 4

2z = -2x + 4

z = -2x/2 + 4/2

z = -x + 2

Answer 30

that's what you should get when you solve for z

Answer 31

then you replace each 'z' you see in equations 1 and 2 with -x+2

Answer 32

that will give you two equations in terms of x and y

Answer 33

do we do this for all the variables?

Answer 34

yes you solve for one variable and plug it into the other equation

Answer 35

that effectively eliminates variables until you're left with one to solve for

Answer 36

so how would i do the next line

Answer 37

what do you get when you plug in z = -x + 2

Answer 38

sorry i messed that up

Answer 39

-x-y(-x+2)=-8
-4x+4y+5(-x+2)=7
2x+2(-x+2)=4?

Answer 40

ignore the last equation

Answer 41

-x - y - z = -8

would turn into

-x - y - (-x + 2) = -8

Answer 42

-4x + 4y + 5z = 7

turns into

-4x + 4y + 5(-x+2) = 7

Answer 43

what next?

Answer 44

solve

-x - y - (-x + 2) = -8

for y

Answer 45

Can I have a hint?

Answer 46

-x - y - (-x + 2) = -8

-x - y + x - 2 = -8

-y - 2 = -8

...

y = ??

Answer 47

close

Answer 48

very close

Answer 49

6

Answer 50

yes y = 6

Answer 51

so now we have to do x?

Answer 52

plug in y = 6 into -4x+4y+5(-x+2)=7 to find x

Answer 53

so -4x+4(6)+5(-x+2)=7 and then solve for x?

Answer 54

yes exactly

Answer 55

okay so -4x+24+5(-x+2)=7
-4x+29(-x+2)=7
how do i work the -x+2

Answer 56

-4x+24+5(-x+2)=7

-4x+24-5x+10=7

-9x+34=7

...

x = ??

Answer 57

3?

Answer 58

good

Answer 59

then use this value of x to find z

Answer 60

so z = -1?

Answer 61

yep

Answer 62

summary: x = 3, y = 6, z = -1

Answer 63

Wow alot of work! Thank you soo much I really appreciate it!!

Answer 64

yw