A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Carissa15

  • one year ago

please help, I have been unable to make any sense from this set of linear equations. Does this mean there is no solution? x-2y+z=0 2y-8z=8 -4x+5y+9z=-9

  • This Question is Closed
  1. texaschic101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    x - 2y + z = 0 --- multiply by 4 -4x + 5y + 9z = -9 ---------------- 4x - 8y + 4z = 0 (result of multiplying by 4) -4x + 5y + 9z = -9 ----------------add -3y + 13z = -9 -3y + 13z = -9 --- multiply by 2 2y - 8z = 8 -- multiply by 3 -------------- -6y + 26z = -18 (result of multiplying by 2) 6y - 24z = 24 (result of multiplying by 3) -------------add 2z = 6 z = 6/2 z = 3 2y - 8z = 8 2y - 8(3) = 8 2y - 24 = 8 2y = 24 + 8 2y = 32 y = 32/2 y = 16 x - 2y + z = 0 x - 2(16) + 3 = 0 x - 32 + 3 = 0 x - 29 = 0 x = 29 now we will check... 2y - 8z = 8 2(16) - 8(3) = 8 32 - 24 = 8 32 = 32 (correct) check... x - 2y + z = 0 29 - 2(16) + 3 = 0 29 - 32 + 3 = 0 32 - 32 = 0 0 = 0 (correct) so x = 29, y = 16, and z = 3

  2. texaschic101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    @Carissa15 .....check it out....any questions ?

  3. texaschic101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    I took my 1st and 3rd equation and eliminated the x. I then took my 2nd equation and the results of my first set of equations, and eliminated the y's....thus finding z. I then subbed z into the 2nd equation and found y. Subbed that into original equation and found x. I then checked my answers and they came out true.

  4. texaschic101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    not really that hard.....just very,very time consuming

  5. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    great. Makes perfect sense. Will work it out on paper myself to make sure I can get the same. Can I check a couple more with you please?

  6. texaschic101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    sure...what ya got ?

  7. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    x-2y+z=0 2y-8z=8 -4x+5y+9z=-9 x+y+z=1 This is throwing me as there are four equations.

  8. texaschic101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    wow...I have never done it with 4....let me see what I can do...this could take awhile.

  9. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    My textbook only covers 2 and some simple 3..

  10. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Could the same values from the last equation work?

  11. texaschic101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    x - 2y + z = 0 --- multiply by 4 -4x + 5y + 9z = -9 ------------- 4x - 8y + 4z = 0 (result of multiplying by 4) -4x + 5y + 9z = -9 --------------add -3y + 13z = -9 -3y + 13z = -9 --- multiply by 2 2y - 8z = 8 -- multiply by 3 ------------- -6y + 26z = -18 (result of multiplying by 2) 6y - 24z = 24 (result of multiplying by 3) ------------- 2z = 6 z = 6/2 z = 3 2y - 8z = 8 2y - 8(3) = 8 2y - 24 = 8 2y = 24 + 8 2y = 32 y = 32/2 y = 16 x - 2y + z = 0 x - 2(16) + 3 = 0 x - 32 + 3 = 0 x - 29 = 0 x = 29 check... 2y - 8z = 8 x - 2y + z = 0 2(16) - 8(3) = 8 29 - 2(16) + 3 = 0 32 - 24 = 8 29 - 32 + 3 = 0 8 = 8 (correct) 0 = 0 (correct) -4x + 5y + 9z = -9 x + y + z = 1 -4(29) + 5(16) + 9(3) = -9 29 + 16 + 3 = 1 -116 + 80 + 27 = -9 48 = 1 (oops....not correct) -116 + 107 = -9 -9 = -9 (correct) I have run into a problem.....for 3 of the equations, my answers are true...but for 1 of them, it is not true. Is x + y + z = 0 written correctly ??

  12. texaschic101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    oops..Is x + y + z = 1 written correctly ??

  13. texaschic101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    weird....I am getting the same answer as the last question

  14. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes it is x+y+z=1

  15. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the first 3 equations are the same as the previous and the 4th is an added equation.

  16. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but the new equation means that for this question the 3 equations do not work as 48 does not equal 1?

  17. texaschic101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    I am not sure about this one....I am so sorry....I think we are gonna have to tag someone

  18. texaschic101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    sweet....john is here :)

  19. johnweldon1993
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No you got it right @texaschic101 I get no solutions for this :)

  20. texaschic101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    my brain is fried right now...lol.

  21. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you so much.

  22. johnweldon1993
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I give you credit, that was the first time I've seen a system of 4 equations O.o haha but awesome work!

  23. texaschic101
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yep....thanks john :)

  24. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I also have this one I am stuck on (due to there not being a number on the right hand side to add/subtract from)

  25. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[2x-y+3z=\alpha \] \[3x+y-5z=\beta \] \[-5x-5y+21z=\gamma \]

  26. johnweldon1993
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh that's interesting Right off the bat though I want to say, you cannot solve a system of equations where you have more variables than equations And here I count 3 equations but a total of 6 variables O.o impossible :)

  27. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that is what isn't making sense to me.

  28. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm, i just found a footnote.... show that the system is inconsistent if

  29. johnweldon1993
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Ahh, lol there ya go

  30. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\gamma \neq 2\alpha-3\beta \]

  31. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oops..

  32. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm, not seeming to get far with this. Any tips?

  33. johnweldon1993
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh sorry, stepped away for a bit Hmm, well lets see \[\large 2x - y + 3z = \alpha\] \[\large 3x + y - 5z = \beta\] \[\large -5x - 5y + 21z = \gamma\] And \(\large \gamma \cancel{=} 2\alpha - 3\beta\)

  34. johnweldon1993
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well if we multiply the first equation by 2 And the second equation by -3 And then add them...what do we get?

  35. johnweldon1993
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Reasoning why I'm doing that, is because it is known we somehow need 2alpha...and we somehow need -3beta...so do that right off the bat And it turns out simpler than you think :D

  36. Carissa15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you @johnweldon1993 sorry, my computer crashed last night. Thank you for your help. Makes much more sense now :)

  37. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.