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

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

---------------------- 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=

-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

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

you need to eliminate y though

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

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

UGHHHHHHHHHHHHH

-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??

nooo

what? :D

this is way too conusing

-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

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

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

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

-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

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

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

that is the first step

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

minus 32

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

-8 x 4 = -32

it said =-8 in the problem thats why

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

where did it say -8

in the pr oblem description first row

thats the row we're using here

it says 0

not on my screen

SHOOT I WAS LOOKING AT THE WRONG PROBLEM

:)

im so sorrry

np

ok so we got -4 x -4y -4z = -32

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

I should really. not have used the equal sign.

before: -x -y -z = -8 after: -4 x -4y -4z = -32

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

okay i get that now what

now, we add that new line with the second row -4 x -4y -4z = -32 -4x +4y +5z = 7 ------------------

so 1z=-25

the x terms are both negative

ohhh so -8x + 1z = -25

yep :)

ok now what:D

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

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

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

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

x

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

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

-6x + 3z = -21

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

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

crap ur right

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

so i multiply

yes, multiply the second row by how much?

the first equation by 2 and the second by 8

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

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

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

ohh i see ill do it ur way

yes now subtract

ok

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

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

yes, problem was 2x + 2z = 4

multiply everything by 4, also the 4

so that is -7z = -41

?????

z = 5.85

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

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

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

okay which equation do i plug z into

any of the two that have only x and z

i would have never noticed that

2x + 2(1) = 4

2x + 2 = 4 2x = 2 x=1

2x + 2z = 4 yes I made an error, though --- z is actually =-1

-25 + 16 = -9 and I wrote 9

yes

yeah i fixed it x=3

[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

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

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

looks good

we can try the values in the other equation: -x -y -z = -8 -(3) -(6) -(-1) = -8 -3-6+1=8

-9+1=8, yep adds up

it adds up because it was -8 in the equation

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