## anonymous one year ago 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

1. 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 ?

2. anonymous

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

3. 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 ?

4. phi

5. anonymous

@phi 6x

6. anonymous

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

7. anonymous

@triciaal

8. anonymous

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

9. 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 ?

10. anonymous

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

11. anonymous

what do i do with the other? @phi

12. triciaal

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

13. triciaal

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

14. anonymous

20x + 2y + 8z = -22

15. triciaal

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

16. anonymous

thank you @triciaal is that equation correct?

17. triciaal

18. anonymous

-8z ?

19. triciaal

yes

20. 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

21. anonymous

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

22. 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

23. 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?

24. phi

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

25. anonymous

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

26. 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

27. anonymous

yeah! that is what I did..

28. 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?

29. anonymous

i got 19x - 6z = -17

30. phi

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

31. 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

32. phi

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

33. anonymous

did i put it in those answers correctly so far?

34. phi

looks good.

35. phi

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

36. 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

37. anonymous

it said add equations together ?

38. 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)

39. anonymous

36x + 6z = -168

40. anonymous

multiplied by 6 ^

41. phi

now we can add the equations

42. anonymous

ok..which equations?

43. phi

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

44. 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

45. anonymous

is this correct? @phi

46. phi

except -168 + -17 is not 185

47. anonymous

-185 ?

48. anonymous

now what about for Q8 ?

49. phi

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

50. 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

51. anonymous

like that? @phi

52. 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

53. phi

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

54. anonymous

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

55. 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

56. anonymous

oh ok

57. anonymous

58. phi

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

59. phi

are you stuck?

60. anonymous

yes! @phi

61. anonymous

just for Q8 idk what to put

62. phi

first we have to do Q7 Q7 solve for second fav

63. 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