Question

Solve the system by substitution ?! SOMEONE HELP PLEASE?!

Answer 1

we have a line with y, z

if we were able to get a second line with y, z
we could get y or z alone

Answer 2

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we have this equation:
2x + 2z = 4

we want a second equation with only x and z in it
because then we can get x= or z=

Answer 3

-x -y -z = -8
-4x +4y +5z = 7

task:
do something to these rows to get a result row that has only x and z in it

Answer 4

if you just added them like they are:
-x -y -z = -8
-4x +4y +5z = 7
-----------------
-5x +3y +4z = -1

Answer 5

you need to eliminate y though

Answer 6

crap so i multiply ??? im not sure how to do this at all

Answer 7

no no addition was correct, however you have to "prepare" the first equation :)

Answer 8

UGHHHHHHHHHHHHH

Answer 9

-x -y -z = -8
-4x +4y +5z = 7

like, if we had multiplied the first row by 4,
then we would get 0y by adding right??

Answer 10

nooo

Answer 11

what? :D

Answer 12

this is way too conusing

Answer 13

-4y + 4y = 0

we have
-y + 4y = 3y

if we had
-4y + 4y it would get 0y

so we have to turn -y
into -4y

Answer 14

yeah I'm sorry, I don't think there's really a way around it though....
im also confused from this stuff lol.

Answer 15

so i just add 4y to that one equation idk i just need step by step

Answer 16

you first need to multiply the first equation by 4
i hope you will be able to see why

Answer 17

-x -y -z = -8
-4x +4y +5z = 7

the goal was to eliminate y, and to eliminate the two y values
have to have the same value

Answer 18

so the very first step is to multiply by 4???????????

Answer 19

yes to mulitply the -x -y -z = -8
row by 4

Answer 20

that is the first step

Answer 21

so that equals -4x -4y -4z = 32

Answer 22

minus 32

Answer 23

okay so what does that equal out to be then??? how can u minus the 32 if there is nothing to minus it from

Answer 24

-8 x 4 = -32

Answer 25

it said =-8 in the problem thats why

Answer 26

-4x -4y -4z = -32

Answer 27

where did it say -8

Answer 28

in the pr oblem description first row

Answer 29

thats the row we're using here

Answer 30

it says 0

Answer 31

not on my screen

Answer 32

http://assets.openstudy.com/updates/attachments/524c5067e4b0e0b65599075a-blahkatherine-1380733064411-help.png

Answer 33

SHOOT I WAS LOOKING AT THE WRONG PROBLEM

Answer 34

:)

Answer 35

im so sorrry

Answer 36

np

Answer 37

ok so we got

-4 x -4y -4z = -32

Answer 38

okay so i thoguht it was -8 x 4 = -32

Answer 39

I should really. not have used the equal sign.

Answer 40

before:
-x -y -z = -8

after:
-4 x -4y -4z = -32

Answer 41

"before" was taken from the problem
"after" is the line multiplied by 4

Answer 42

okay i get that now what

Answer 43

now, we add that new line with the second row

-4 x -4y -4z = -32
-4x +4y +5z = 7
------------------

Answer 44

so 1z=-25

Answer 45

the x terms are both negative

Answer 46

ohhh so -8x + 1z = -25

Answer 47

yep :)

Answer 48

ok now what:D

Answer 49

Progress so far:
[x] 1. get a second x,z equation by elimination
[ ] 2. add the two x,z equations and get z=
[ ] 3. substitute z in one of the x,z equations

Answer 50

we now have two x, z equations
-8x + 1z = -25 (just calculated)
2x + 2z = 4 (problem description)

we should add them in such a way that one of the variables is eliminated

Answer 51

subtract???????????

Answer 52

do you want to eliminate x or z first
it doesn't matter which one

Answer 53

x

Answer 54

then because one of the X is negative we would add instead of subtract

Answer 55

-8x + 1z = -25
2x + 2z = 4

Answer 56

-6x + 3z = -21

Answer 57

true

this is a legal operation. HOWEVER, it did not eliminate x :)

Answer 58

we need to make the Xes the same "size" before adding, to eliminate

Answer 59

crap ur right

Answer 60

-8x + 1z = -25
2x + 2z = 4

Answer 61

so i multiply

Answer 62

yes, multiply the second row
by how much?

Answer 63

the first equation by 2 and the second by 8

Answer 64

possible. since 2/8 can be reduced to 1/4
you can also multiply the first one by 1 and the second by 4

Answer 65

-8x + 1z = -25
4(2x) +4(2z) = 4(4)

Answer 66

so its
16x + 2z = -50
16x + 16z = 32

Answer 67

ohh i see ill do it ur way

Answer 68

yes now subtract

Answer 69

ok

Answer 70

when u said " -8x + 1z = -25 4(2x) +4(2z) = 4(4) " <---- is there supposed to be a 4

Answer 71

-8x + 1z = -25
8x +8z = 16

Answer 72

yes, problem was 2x + 2z = 4

Answer 73

multiply everything by 4, also the 4

Answer 74

so that is -7z = -41

Answer 75

?????

Answer 76

z = 5.85

Answer 77

no we add instead of subtract because -8x and 8x

Answer 78

-8x + 1z = -25
8x +8z = 16
--------------
9z = 9
z = 1

Answer 79

error, 9z = -9
so z = -1

Answer 80

okay which equation do i plug z into

Answer 81

any of the two that have only x and z

Answer 82

i would have never noticed that

Answer 83

2x + 2(1) = 4

Answer 84

2x + 2 = 4

2x = 2
x=1

Answer 85

2x + 2z = 4

yes I made an error, though --- z is actually =-1

Answer 86

-25 + 16 = -9 and I wrote 9

Answer 87

yes

Answer 88

yeah i fixed it x=3

Answer 89

[x] 1. get a second x,z equation
[x] 2. add the two x,z equations and get z=
[x] 3. substitute z in one of the x,z equations

ok now that we have x and z value
we can just plug those in any of the two first equations to get y

Answer 90

the first equations according to problem:
-x -y -z = -8
-4x +4y +5z = 7

Answer 91

we need an equation that has y in it otherwise we can't solve for y

Answer 92

looks good

Answer 93

we can try the values in the other equation:

-x -y -z = -8
-(3) -(6) -(-1) = -8
-3-6+1=8

Answer 94

-9+1=8, yep adds up

Answer 95

it adds up because it was -8 in the equation