Question

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

Answer 1

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 ?

Answer 2

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

Answer 3

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 ?

Answer 4

can you add 5x+x ?

Answer 5

@phi 6x

Answer 6

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

Answer 7

@triciaal

Answer 8

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

Answer 9

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 ?

Answer 10

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

Answer 11

what do i do with the other? @phi

Answer 12

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

Answer 13

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

Answer 14

20x + 2y + 8z = -22

Answer 15

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

Answer 16

thank you @triciaal is that equation correct?

Answer 17

not exactly watch your signs

Answer 18

-8z ?

Answer 19

yes

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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?

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

yeah! that is what I did..

Answer 28

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?

Answer 29

i got 19x - 6z = -17

Answer 30

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

Answer 31

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

Answer 32

for Q4 we have these equations
6x + z = -28
19x - 6z = -17

for Q5, pick z as the "favorite variable"

Answer 33

did i put it in those answers correctly so far?

Answer 34

looks good.

Answer 35

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

Answer 36

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

Answer 37

it said add equations together ?

Answer 38

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)

Answer 39

36x + 6z = -168

Answer 40

multiplied by 6 ^

Answer 41

now we can add the equations

Answer 42

ok..which equations?

Answer 43

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

Answer 44

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

Answer 45

is this correct? @phi

Answer 46

except -168 + -17 is not 185

Answer 47

-185 ?

Answer 48

now what about for Q8 ?

Answer 49

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

Answer 50

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

Answer 51

like that? @phi

Answer 52

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

Answer 53

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

Answer 54

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

Answer 55

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

Answer 56

oh ok

Answer 57

what about Q8 ?

Answer 58

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

Answer 59

are you stuck?

Answer 60

yes! @phi

Answer 61

just for Q8 idk what to put

Answer 62

first we have to do Q7
Q7 solve for second fav

Answer 63

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