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NY,NY

HELPPP ME STUDY! solve algebraically for a and b and check: 3a+5b=4 4a+3b=-2

  • one year ago
  • one year ago

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  1. goformit100
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    You can use Matrix method for solving these two equations simultaneously

    • one year ago
  2. NY,NY
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    i only know substitution, graphing, and elimination method and those are the only methods i can use.

    • one year ago
  3. darkprince14
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    try eliminating either a or b

    • one year ago
  4. darkprince14
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    If you're looking for the point of intersection or the solution to those two then that's helpful if not, sorry, i have no clue what to do next ..

    • one year ago
  5. NY,NY
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    i need to find the value of a and b, not find the solution. like get a or b by itself.

    • one year ago
  6. darkprince14
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    how about let a = 0 or something like that...

    • one year ago
  7. NY,NY
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    not working :(

    • one year ago
  8. theEric
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    Here's the plan; try to "get a in terms of b" (or "b in terms of a"). Really, I mean try to solve for a, so that it equals something that involves b (or solve for b so that it equals something that involves a).

    • one year ago
  9. NY,NY
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    yeah, i know. but how do i do that?

    • one year ago
  10. theEric
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    You can look at either equation, and solve for either variable. It's up to you!

    • one year ago
  11. theEric
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    It's all fair game in this problem. So pick and equation and pick a variable to solve for!

    • one year ago
  12. NY,NY
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    ok, 3a+5b=4. let's solve for a.

    • one year ago
  13. theEric
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    Okay, you start! I'll watch.

    • one year ago
  14. theEric
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    Unless you want to workon it together now; we can do that.

    • one year ago
  15. theEric
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    work on*

    • one year ago
  16. NY,NY
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    yeah, let's work on it together.

    • one year ago
  17. theEric
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    Alright. When equations aren't too complex, a great starting point is getting the terms containing variable you're solving for, a, on the opposite side of all the other terms. So look at 3a+5b=4. Which term (containing a) do we want to it's own side?

    • one year ago
  18. NY,NY
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    3a.

    • one year ago
  19. NY,NY
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    3a= -5b+4

    • one year ago
  20. theEric
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    I agree! And it's with 5b, which we need to get rid of. And it appears you know how to do that! Good! So now a is still stuck with something; it's being multiplied by 3! So can you fix that, too?

    • one year ago
  21. NY,NY
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    \[a= \frac{ 5b+4 }{ 3 }\]

    • one year ago
  22. theEric
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    close! You forgot your sign of 5b! You had it right before! I'm guessing you were distracted by Open Study's fancy equation thing, but I don't know.

    • one year ago
  23. theEric
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    so a=(-5b+4)/3

    • one year ago
  24. NY,NY
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    oopssss. i meant -5b*

    • one year ago
  25. NY,NY
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    yeahh

    • one year ago
  26. theEric
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    \[a=\frac{-5b+4}{3}\]Haha, that's fine! So we solved for a in that one equation, 3a+5b=4. a is always a is always (-5b+4)/3. So we can substitute it into another a's place. Try it in the other equation, 4a+3b=-2. the a will be replaced and the only variable in the equation will be b. The we can solve for b!

    • one year ago
  27. theEric
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    So, start by substitution!

    • one year ago
  28. NY,NY
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    -20b+16/3+3b=-2

    • one year ago
  29. theEric
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    Make sure you type (-20b+16)/3 + 3b = -2 ! I see you factored correctly, but the way you wrote it it didn't look like it was all divided by 3, though it really was! :)

    • one year ago
  30. theEric
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    So\[\frac{-20b+16}{3}+3b = -2\]

    • one year ago
  31. NY,NY
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    multiply by 3?

    • one year ago
  32. theEric
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    Yeah, I'd do that!

    • one year ago
  33. theEric
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    Just so that left-most b isn't divided by it.

    • one year ago
  34. NY,NY
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    -20b+16+3b=-6?

    • one year ago
  35. theEric
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    So\[3(\frac{-20b+16}{3}+3b)=3(-2)\]

    • one year ago
  36. theEric
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    Common mistake! Don't worry! You just have to remember to multiply each entire side by 3. That way you're doing the same thing to each side, so that the two new sides will still be equal.

    • one year ago
  37. NY,NY
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    i multiplied by 3 to -20b + 16 so that canceled the 3 out, and then i multiplied the -2 by 3, giving -6. what i do wrong?

    • one year ago
  38. theEric
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    You have to multiply 3b by 3 as well!

    • one year ago
  39. theEric
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    it becomes 9b!

    • one year ago
  40. theEric
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    So -20b+16+9b=-6 :)

    • one year ago
  41. theEric
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    I'm sure you'll see it soon.

    • one year ago
  42. NY,NY
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    ohhh. wow, yeah. b=2?

    • one year ago
  43. theEric
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    -20b+16+9b=-6 -20b+9b=-22 -11b=-22 22=11b 22/11=b 2=b Yeah!

    • one year ago
  44. theEric
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    I had to work it out to check, but we got the same thing.

    • one year ago
  45. NY,NY
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    yay :D thanks eric :D yur awesome :D

    • one year ago
  46. theEric
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    Sorry for the wait, Open Study glitched :P Recap, we solved for "a in terms of b" and we solved for b. Now we know b and can now solve for a!

    • one year ago
  47. theEric
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    My pleasure! Thank you for doing your part! You did great!

    • one year ago
  48. theEric
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    \[a=\frac{-5b+4}{3}=\frac{-5(2)+4}{3}\] and compute... finale!

    • one year ago
  49. NY,NY
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    thanks :D

    • one year ago
  50. NY,NY
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    i just hope i do good on the quiz tomorrow...

    • one year ago
  51. NY,NY
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    a=-10+4/3 a=-6/3 a=-2

    • one year ago
  52. theEric
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    My pleasure. Did you get a = 2?

    • one year ago
  53. theEric
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    Best of luck! Tag me in any other questions you have, or you can ask them here. But the most important thing in these an dmany other math problems is planning! Knowing what you will do. This technique we used is good for this situation.

    • one year ago
  54. theEric
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    Haha!! Caught me! -2 ! :D

    • one year ago
  55. theEric
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    Serves me right for trying to do it in my head.

    • one year ago
  56. theEric
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    My responses are out of order. Open Stud is scrambled, it seems.

    • one year ago
  57. NY,NY
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    yeah. open study is being really laggy today. if i can just finish up my science homework, ill bring up some more questions to study with. thanks again :D and bye for now.

    • one year ago
  58. theEric
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    I'm glad it's not just me! No problem. Good luck with everything!

    • one year ago
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