A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. 4x-8y=48 11x+3y=-105.5

  • This Question is Closed
  1. campbell_st
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    simplify 4x - 8y = 48 to x - 2y = 12 (1) and 11x + 3y = -105.5 (2) then use (1) x 11 - (2) which will eliminate x and solve for y

  2. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yikes another one with decimals!

  3. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you got this?

  4. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no not really

  5. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hold on we can do it

  6. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[x - 2y = 12 \] \[11x+3y=-105.5\]

  7. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    multiply the first equation by -11 and add to the second one

  8. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok is it 2y or 3y

  9. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[-11x+22y=132\] \[11x+3y=-105.5\]

  10. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is it suppose to be x-2y or x-3y?

  11. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    first equation simplifies by dividing by 4, giving you \[x-2y=12\]

  12. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh ok

  13. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now add the two equations together

  14. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the x terms add up to zero and you get \[25y=26.5\] if my arithmetic is correct

  15. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    damn i screwed up again!

  16. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok lol we can fix it

  17. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you multiply the first one by -11

  18. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[-11x+22y=-132\]

  19. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i forgot the negative on the right hand side

  20. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so where does that come in

  21. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[-11x+22y=-132\] \[11x+3y=-105.5\]

  22. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok lets go slow

  23. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you have \[x-2y=12\] \[11x+3y=-105.5\] right?

  24. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  25. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and you want to eliminate one of the variables so you can solve on equation with one variable

  26. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i am confused on what comes first can you lay it out the way it suppose to be

  27. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes it looks like this

  28. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  29. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[x-2y=12\] \[11x+3y=-105.5\] then \[(-11)\times (x-2y)=(-11)\times 12\] \[11x+3y=-105.5\] then \[-11x+22y=-132\] \[11x+3y=-105.5\]

  30. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you have to figure out for yourself that if you multiply the first equation across by -11 and then add, the x terms will drop out when you add the two equations. finding what to multiply by is up to you.

  31. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i am lost

  32. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now add and get \[25y=-235.5\] so now \[x=-237.5\div 25=-9.5\]

  33. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    why don't we try an easy one first. suppose i see \[x+y=1\] \[x-y=7\]how can i find x and y?

  34. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if you add the two equations together you get \[2x=8\] because you get \[x+y+x-y=1+7\] \[2x=8\]

  35. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  36. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now i have one variable and one equation, so easy to solve, if \[2x=8\] then \[x=4\] and if i know \[x=4\] then i know \[y=3\] because the first equation says \[x+y=7\] so \[4+y=7\] and therefore \[y=3\]

  37. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    unfortunately in your problem if i simply add, nothing drops out. so you have to arrange it so that one of the variables will go away when you add

  38. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok when it comes to my problem i get really lost

  39. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so for example if i see \[2x+3y=7\] \[x-y=1\] have to get rid of one variable by multiplying one equation all the way across by a number that will make one of the variables go away when i add

  40. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so i could multiply the second equation by 3 and get \[2x+3y=7\] \[3x-3y=3\] and now it is easy add to get \[5x=10\] so \[x=2\]

  41. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    in your problem you have \[x-2y=12\] \[11x+3y=-105.5\]

  42. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    to make one of the variables go, multiply the top one by -11 so you will have \[-11x\] in the first equation and \[11x\] in the second one, and they will add up to zero

  43. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we have to multiply EVERYTHING by -11 in the first equation and we get \[-11x+22y=-132\] \[11x+3y=-105.5\]

  44. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now when you add there will be no more x's

  45. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok is that the first part or the second part

  46. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i am not sure what you mean

  47. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    step one was to turn \[4x-8y=48\] into \[x-2y=4\]

  48. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    step two was to multiply by -11 to get \[-11x+22y=-132\]

  49. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    step 3 is to add it to the second equation. the x's add to zero and you get \[25y=-137.5\]

  50. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    step 4 is to solve for y via \[y=-237.5\div 25\] \[y=-9.5\]

  51. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    typo in step 3, should have been \[25y=-237.5\]

  52. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and finally to find x, replace y by -9.5 in either equation

  53. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok with x would you divide by 2 for the first step as well

  54. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[x-2y=12\] \[x-2\times (-9.5)=12\] \[x+19=12\] \[x=12-19\] \[x=-7\]

  55. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you can divide the first equation by 4, because each term has a common factor of 4 just makes it easier to work with

  56. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    in general no, you do not divide as a first step. in general you see what you can multiply one equation by to make one variable drop out when you add the two equations

  57. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok still a little lost but getting the hang of it

  58. 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.