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NY,NY

  • 2 years ago

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

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  1. goformit100
    • 2 years ago
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    You can use Matrix method for solving these two equations simultaneously

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

  3. darkprince14
    • 2 years ago
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    try eliminating either a or b

  4. darkprince14
    • 2 years ago
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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 ..

  5. NY,NY
    • 2 years ago
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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.

  6. darkprince14
    • 2 years ago
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    how about let a = 0 or something like that...

  7. NY,NY
    • 2 years ago
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    not working :(

  8. theEric
    • 2 years ago
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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).

  9. NY,NY
    • 2 years ago
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    yeah, i know. but how do i do that?

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

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

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

  13. theEric
    • 2 years ago
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    Okay, you start! I'll watch.

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

  15. theEric
    • 2 years ago
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    work on*

  16. NY,NY
    • 2 years ago
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    yeah, let's work on it together.

  17. theEric
    • 2 years ago
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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?

  18. NY,NY
    • 2 years ago
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    3a.

  19. NY,NY
    • 2 years ago
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    3a= -5b+4

  20. theEric
    • 2 years ago
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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?

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

  22. theEric
    • 2 years ago
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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.

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

  24. NY,NY
    • 2 years ago
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    oopssss. i meant -5b*

  25. NY,NY
    • 2 years ago
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    yeahh

  26. theEric
    • 2 years ago
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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!

  27. theEric
    • 2 years ago
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    So, start by substitution!

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

  29. theEric
    • 2 years ago
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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! :)

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

  31. NY,NY
    • 2 years ago
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    multiply by 3?

  32. theEric
    • 2 years ago
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    Yeah, I'd do that!

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

  34. NY,NY
    • 2 years ago
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    -20b+16+3b=-6?

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

  36. theEric
    • 2 years ago
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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.

  37. NY,NY
    • 2 years ago
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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?

  38. theEric
    • 2 years ago
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    You have to multiply 3b by 3 as well!

  39. theEric
    • 2 years ago
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    it becomes 9b!

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

  41. theEric
    • 2 years ago
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    I'm sure you'll see it soon.

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

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

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

  45. NY,NY
    • 2 years ago
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    yay :D thanks eric :D yur awesome :D

  46. theEric
    • 2 years ago
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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!

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

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

  49. NY,NY
    • 2 years ago
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    thanks :D

  50. NY,NY
    • 2 years ago
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    i just hope i do good on the quiz tomorrow...

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

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

  53. theEric
    • 2 years ago
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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.

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

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

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

  57. NY,NY
    • 2 years ago
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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.

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

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