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MiaKitty Group Title

6.03] Part 1: Decide whether you would use the graphing, substitution, or elimination method to solve the following system of equations. Explain, in complete sentences, why you chose that method. Part 2: Solve the following system of equations and show all of your work. 4x + 3y = -1 3x + y = 3

  • one year ago
  • one year ago

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  1. onmng314 Group Title
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    I would help you, BUT you hated my answer to your last question like this ;)

    • one year ago
  2. MiaKitty Group Title
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    Oh, that is okay, I did not hete your answer anyhow. :) This is a new question, so it doesn't matter, If you post it, I can work it out. :)

    • one year ago
  3. onmng314 Group Title
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    OK. The first thing to understand is that you have two linear equations. They are lines. They expand across all of (X,Y) space. When you are asked to solve a system of equations, all they want you to do is figure out whether the two equations have any solutions. In other words, do the two lines intersect somewhere? Are you with me so far?

    • one year ago
  4. MiaKitty Group Title
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    Yes, but the thing is I don't knoiw, because I don't like inequality questions, they can be anything!

    • one year ago
  5. onmng314 Group Title
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    Miapoopoopoo, They aren't inequality questions :) Now I will help you proceed. NOTE: The form of the equations you have are USELESS. The information is in there, but it is difficult to see it. Solution: Get your two equations into slope intercept form, namely y=mx + b where m is your slope and b is the point where the line intersects the Y axis. Can you get the equations into y= (everything else)?

    • one year ago
  6. onmng314 Group Title
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    BEFORE you reply. Where I am taking you is toward the GRAPHING method. I can help you with any method you choose, though. You tell me what you would like to do...

    • one year ago
  7. MiaKitty Group Title
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    I don't know, maybe elimination or substitution?; :)

    • one year ago
  8. onmng314 Group Title
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    I prefer ELIMINATION. Let's do that.

    • one year ago
  9. MiaKitty Group Title
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    Okay, thx. :)

    • one year ago
  10. onmng314 Group Title
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    Quick question: Did they happen to give you the answer to the problem ahead of time? I recall you were not able to check the last time I helped ;)

    • one year ago
  11. MiaKitty Group Title
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    No, actually, you are supposed to solve it, and then they tell you if you r right. :)

    • one year ago
  12. onmng314 Group Title
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    That is no problem :)

    • one year ago
  13. MiaKitty Group Title
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    :D

    • one year ago
  14. onmng314 Group Title
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    4x+3y = -1 3x+ y = 3 I really really want you to realize that you can do ANYTHING to these equations, as long as you do the same thing to both sides. That maintains the equality. The key is to change the top and the bottom in such a way so as to make a cancellation (ELIMINATION) possible. Still following?

    • one year ago
  15. MiaKitty Group Title
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    Yes, :)

    • one year ago
  16. onmng314 Group Title
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    COOL! Now can you think of something we can do to one equation (or BOTH) to make a cancellation possible? The key is to make a cancellation possible in X or in Y. 4x +3y = -1 3x + y = 3 For example, if we multiply the top equation by (-1) and multiply the bottom equation by (3) we can get the Y value to cancel. We will eliminate it.

    • one year ago
  17. onmng314 Group Title
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    (-1)(4x+3y=-1) (3) (3x+y = 3) Notice I am multiplying BOTH sides of each equation by the number we picked. Can you see that?

    • one year ago
  18. MiaKitty Group Title
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    Yes. :)

    • one year ago
  19. onmng314 Group Title
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    Now let's multiply by distributing the numbers we picked. -4x-3y=1 9x+3y=9 Is that what you got when you multiplied (distributed)?

    • one year ago
  20. MiaKitty Group Title
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    Yes., that's what you get. :) Had to look at the problem for a sec. :)

    • one year ago
  21. onmng314 Group Title
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    For Elimination method, you have to "add" the two equations. I prefer to say "combine" the equations. -4x-3y=1 9x+3y=9 ------------ 5x+0 =10 OR 5x=10

    • one year ago
  22. onmng314 Group Title
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    Now that we did the appropriate Elimination, can you figure out what X is?

    • one year ago
  23. MiaKitty Group Title
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    2?

    • one year ago
  24. onmng314 Group Title
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    CORRECT!

    • one year ago
  25. onmng314 Group Title
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    So we figured out the value for X. Great! Now what? Remember, we solved a SYSTEM of equations. Our value of X is a "solution" for each equation. To figure out Y, simply plug your X into either equation. Now make it happen and tell me what you get...

    • one year ago
  26. MiaKitty Group Title
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    Ok, thx so much! :D

    • one year ago
  27. onmng314 Group Title
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    We aren't done :)

    • one year ago
  28. MiaKitty Group Title
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    I know, let's see, hold on a sec...

    • one year ago
  29. MiaKitty Group Title
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    Is it -3?

    • one year ago
  30. onmng314 Group Title
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    YES!

    • one year ago
  31. onmng314 Group Title
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    So you figured out that X=2 and Y=-3 We know better so we also know that the point (2,-3) is the point at which both lines intersect.

    • one year ago
  32. MiaKitty Group Title
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    Ok, is that it?

    • one year ago
  33. onmng314 Group Title
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    Now verify using the link below. Start liking Wolfram :) http://www.wolframalpha.com/input/?i=4x%2B3y%3D-1%2C+3x%2By%3D3 Note the two lines and one point of intersection. Also note the solutions they give you for X and for Y. THE SAME!

    • one year ago
  34. MiaKitty Group Title
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    Ok, thx! LOL! I will check it out!

    • one year ago
  35. onmng314 Group Title
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    Enter your answers in the way they ask. IF they ask for an ordered pair (X,Y) give them that. If they ask for X= and Y= give them that.

    • one year ago
  36. MiaKitty Group Title
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    Ok. :)

    • one year ago
  37. onmng314 Group Title
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    Do it and report back here with the results. MK.

    • one year ago
  38. MiaKitty Group Title
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    Hey, they say it is right! :D

    • one year ago
  39. onmng314 Group Title
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    So I was probably right last time, too, huh? LOL

    • one year ago
  40. MiaKitty Group Title
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    LOL, :) Oh well, :)

    • one year ago
  41. MiaKitty Group Title
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    You got a medal this time, 2 from me. :)

    • one year ago
  42. onmng314 Group Title
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    I hope you learned a little about how to THINK about this kind of problem. Sure it took a long time, but it might help during exams. You are welcome and good luck :)

    • one year ago
  43. MiaKitty Group Title
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    thx, lol! :D

    • one year ago
  44. MiaKitty Group Title
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    are you in calculus?

    • one year ago
  45. onmng314 Group Title
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    Yes.

    • one year ago
  46. onmng314 Group Title
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    It is the bomb :)

    • one year ago
  47. MiaKitty Group Title
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    So, you like it, I'm dreading it!

    • one year ago
  48. onmng314 Group Title
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    Nooooooo! It was the first time I saw some real application of math. All the math you have done leading until now is all in preparation for Calculus. I used to hate math. Now I love it. I'm in Cal 2. Cal 3 next semester.

    • one year ago
  49. MiaKitty Group Title
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    Really, that is so cool! :D I hope I do good in it, lol!

    • one year ago
  50. onmng314 Group Title
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    Very practical stuff. It sounds difficult, but when you really get down to it, it is all about ADDING ( an infinite amount). That is the hard part. lol.

    • one year ago
  51. MiaKitty Group Title
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    oh, wow, whattopics do you learn, lol?

    • one year ago
  52. onmng314 Group Title
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    Well, I am signing off now. If you ever get stuck, shoot me an email. Byeeeeeeeeee

    • one year ago
  53. MiaKitty Group Title
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    Ok, byeee!

    • one year ago
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