anonymous
  • anonymous
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
Mathematics
schrodinger
  • schrodinger
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phi
  • 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
  • anonymous
@phi 4x + 5z = -28 ??
phi
  • 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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phi
  • phi
can you add 5x+x ?
anonymous
  • anonymous
@phi 6x
anonymous
  • anonymous
@phi 6x + z = -28 now what?
anonymous
  • anonymous
anonymous
  • anonymous
I dont know what to do now for Q5-Q8 ?? :(
phi
  • 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
  • anonymous
multiply just 10x + y - 4z = -11 by 2 ?
anonymous
  • anonymous
what do i do with the other? @phi
triciaal
  • triciaal
You will add it to the new equation you get when you do the multiplication
triciaal
  • triciaal
so go ahead and do the multiplication and show what you get
anonymous
  • anonymous
20x + 2y + 8z = -22
triciaal
  • triciaal
sure he will be back he is going through all the steps with you
anonymous
  • anonymous
thank you @triciaal is that equation correct?
triciaal
  • triciaal
not exactly watch your signs
anonymous
  • anonymous
-8z ?
triciaal
  • triciaal
yes
anonymous
  • 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
  • anonymous
like how do i explain and set that all up into these questions?
anonymous
  • 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
  • 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
  • phi
oops , we are doing Q3 Q2 is what we got from the first two equations, up above.
anonymous
  • anonymous
so Q3 is 6x + z = -28 ??
phi
  • 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
  • anonymous
yeah! that is what I did..
phi
  • 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
  • anonymous
i got 19x - 6z = -17
phi
  • phi
ok, that is the last part of the answer for Q3
anonymous
  • 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
  • phi
for Q4 we have these equations 6x + z = -28 19x - 6z = -17 for Q5, pick z as the "favorite variable"
anonymous
  • anonymous
did i put it in those answers correctly so far?
phi
  • phi
looks good.
phi
  • phi
for Q6 6x + z = -28 <--- multiply all terms by 6 19x - 6z = -17
anonymous
  • 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
  • anonymous
it said add equations together ?
phi
  • 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
  • anonymous
36x + 6z = -168
anonymous
  • anonymous
multiplied by 6 ^
phi
  • phi
now we can add the equations
anonymous
  • anonymous
ok..which equations?
phi
  • phi
19x - 6z = -17 36x + 6z = -168
anonymous
  • 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
  • anonymous
is this correct? @phi
phi
  • phi
except -168 + -17 is not 185
anonymous
  • anonymous
-185 ?
anonymous
  • anonymous
now what about for Q8 ?
phi
  • phi
yes, so 55x= -185 divide both sides by 55 \[ x = - \frac{185}{55}= - \frac{37}{11} \]
anonymous
  • 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
  • anonymous
like that? @phi
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
  • phi
for A7, use 19x - 6z = -17 replace x with -37/11
anonymous
  • anonymous
lol i am confused now ... can u copy and paste that Q&A format in the beginning so i can see?
phi
  • 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
  • anonymous
oh ok
anonymous
  • anonymous
what about Q8 ?
phi
  • phi
for A7, use 19x - 6z = -17 replace x with -37/11
phi
  • phi
are you stuck?
anonymous
  • anonymous
yes! @phi
anonymous
  • anonymous
just for Q8 idk what to put
phi
  • phi
first we have to do Q7 Q7 solve for second fav
phi
  • 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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