Can someone set up this question for me? I am really struggling/:
5x - 2y + 3z = -23
-x - 2y + 2z = 5
10x + y - 4z = -11
Q1 choose a fav variable
A1
Q2 pick a pair of equations, eliminate the fav variable
A2
Q3 pick another pair, eliminate that same fav
A3
Q4 now you have only 2 variables in 2 equations, like a+b=7 & a-2b=13
A4
Q5 pick a second fav
A5
Q6 add equations together and eliminate it
A6
Q7 solve for second fav
A7
Q8 sub second fav into equation and find last variable
A8

- anonymous

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- phi

How about starting with y
and the first two equations
5x - 2y + 3z = -23
-x - 2y + 2z = 5
subtract the bottom equation from the top equation
can you do that ?

- anonymous

@phi 4x + 5z = -28 ??

- phi

the easiest (or at least likely to make mistakes) is to first multiply the 2nd equation by -1
that means multiply both sides and all terms by -1
-1*(-x - 2y + 2z ) = -1*5
distribute the -1. we get
\[-1\cdot -x + -1\cdot-2y + -1\cdot2z = -5\\
x+2y -2z = -5 \]
now we add, term by term the top equation and this new equation
5x - 2y + 3z = -23
x+ 2y - 2z = -5
what do you get ?

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## More answers

- phi

can you add 5x+x ?

- anonymous

@phi 6x

- anonymous

@phi 6x + z = -28 now what?

- anonymous

@triciaal

- anonymous

I dont know what to do now for Q5-Q8 ?? :(

- phi

ok that looks good.
now pick the 2nd and 3rd equations
-x - 2y + 2z = 5
10x + y - 4z = -11
and we again want to "get rid of y"
multiply the second equation in that pair by 2 (all terms)
can you do that ?

- anonymous

multiply just 10x + y - 4z = -11 by 2 ?

- anonymous

what do i do with the other? @phi

- triciaal

You will add it to the new equation you get when you do the multiplication

- triciaal

so go ahead and do the multiplication and show what you get

- anonymous

20x + 2y + 8z = -22

- triciaal

sure he will be back he is going through all the steps with you

- anonymous

thank you @triciaal is that equation correct?

- triciaal

not exactly watch your signs

- anonymous

-8z ?

- triciaal

yes

- anonymous

so now that i have done that, what do i put into this?
Q5 pick a second fav
A5
Q6 add equations together and eliminate it
A6
Q7 solve for second fav
A7
Q8 sub second fav into equation and find last variable
A8

- anonymous

like how do i explain and set that all up into these questions?

- anonymous

because I have this so far.. does it look correct?
5x - 2y + 3z = -23
-x - 2y + 2z = 5
10x + y - 4z = -11
Q1 choose a fav variable
A1 y
Q2 pick a pair of equations, eliminate the fav variable
A2 5x - 2y + 3z = -23 - -x - 2y + 2z = 5 = 4x + 5z = -28
Q3 pick another pair, eliminate that same fav
A3 6x + z = -28
Q4 now you have only 2 variables in 2 equations, like a+b=7 & a-2b=13
A4 4x + 5z = -28 & 6x + z = -28

- phi

we are doing Q2
we picked the 2nd and 3rd equations
-x - 2y + 2z = 5
10x + y - 4z = -11
. You multiplied the 2nd of that pair by 2.
you now have the equations
-x - 2y + 2z = 5
20x + 2y - 8z = -22
now add those two equations. what do you get?

- phi

oops , we are doing Q3
Q2 is what we got from the first two equations, up above.

- anonymous

so Q3 is 6x + z = -28 ??

- phi

FYI the answer for Q2
Here are the steps
5x - 2y + 3z = -23
-x - 2y + 2z = 5 <-- multiply by -1 and add to the top equation. we get
6x + z = -28

- anonymous

yeah! that is what I did..

- phi

for Q3
we picked the 2nd and 3rd equations
-x - 2y + 2z = 5
10x + y - 4z = -11 .
You multiplied the 2nd of that pair by 2.
you now have the equations
-x - 2y + 2z = 5
20x + 2y - 8z = -22
now add those two equations. what do you get?

- anonymous

i got 19x - 6z = -17

- phi

ok, that is the last part of the answer for Q3

- anonymous

Q1 choose a fav variable
A1 y
Q2 pick a pair of equations, eliminate the fav variable
A2 5x - 2y + 3z = -23 - -x - 2y + 2z = 5 = 4x + 5z = -28
Q3 pick another pair, eliminate that same fav
A3 -x - 2y + 2z = 5 + 20x + 2y - 8z = -22 = 19x - 6z = -17

- phi

for Q4 we have these equations
6x + z = -28
19x - 6z = -17
for Q5, pick z as the "favorite variable"

- anonymous

did i put it in those answers correctly so far?

- phi

looks good.

- phi

for Q6
6x + z = -28 <--- multiply all terms by 6
19x - 6z = -17

- anonymous

Q4 now you have only 2 variables in 2 equations, like a+b=7 & a-2b=13
A4 6x + z = -28 & 19x - 6z = -17
Q5 pick a second fav
A5 z
Q6 add equations together and eliminate it
A6 6x + z = -28 + 19x - 6z = -17 = 25x - 5z = -45

- anonymous

it said add equations together ?

- phi

unless there is a typo in the original equations, we can't just add them
first we multiply the first one by 6 (this will give us a 6z term that will cancel the -6z in the other equation)

- anonymous

36x + 6z = -168

- anonymous

multiplied by 6 ^

- phi

now we can add the equations

- anonymous

ok..which equations?

- phi

19x - 6z = -17
36x + 6z = -168

- anonymous

Q5 pick a second fav
A5 z
Q6 add equations together and eliminate it
A6 36x + 6z = -168 + 19x - 6z = -17
Q7 solve for second fav
A7 55x = 185

- anonymous

is this correct? @phi

- phi

except -168 + -17 is not 185

- anonymous

-185 ?

- anonymous

now what about for Q8 ?

- phi

yes, so
55x= -185
divide both sides by 55
\[ x = - \frac{185}{55}= - \frac{37}{11} \]

- anonymous

5x - 2y + 3z = -23
-x - 2y + 2z = 5
10x + y - 4z = -11
Q1 choose a fav variable
A1 y
Q2 pick a pair of equations, eliminate the fav variable
A2 5x - 2y + 3z = -23 - -x - 2y + 2z = 5 = 4x + 5z = -28
Q3 pick another pair, eliminate that same fav
A3 -x - 2y + 2z = 5 + 20x + 2y - 8z = -22 = 19x - 6z = -17
Q4 now you have only 2 variables in 2 equations, like a+b=7 & a-2b=13
A4 6x + z = -28 & 19x - 6z = -17
Q5 pick a second fav
A5 z
Q6 add equations together and eliminate it
A6 36x + 6z = -168 + 19x - 6z = -17 x= -37/11
Q7 solve for second fav
A7 55x = -185
Q8 sub second fav into equation and find last variable
A8

- anonymous

like that? @phi

- phi

yes, but when you show the equations, you should put them on separate lines
something like this:
A6 36x + 6z = -168
+ 19x - 6z = -17
-------------------
55x = -185
x = -185/55 = -37/11

- phi

for A7, use
19x - 6z = -17
replace x with -37/11

- anonymous

lol i am confused now ... can u copy and paste that Q&A format in the beginning so i can see?

- phi

you wrote
Q6 add equations together and eliminate it
A6 36x + 6z = -168 + 19x - 6z = -17 x= -37/11
it would be clearer if you wrote it as
A6 36x + 6z = -168
+ 19x - 6z = -17
-------------------
55x = -185
x = -185/55 = -37/11

- anonymous

oh ok

- anonymous

what about Q8 ?

- phi

for A7, use 19x - 6z = -17 replace x with -37/11

- phi

are you stuck?

- anonymous

yes! @phi

- anonymous

just for Q8 idk what to put

- phi

first we have to do Q7
Q7 solve for second fav

- phi

to do that we start with one of the equations from A4
for example, we can use
6x + z = -28
x is -37/11
replace x with that number. we want to find what z is

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