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MiaKitty

  • 2 years ago

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

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  1. onmng314
    • 2 years ago
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    I would help you, BUT you hated my answer to your last question like this ;)

  2. MiaKitty
    • 2 years ago
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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. :)

  3. onmng314
    • 2 years ago
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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?

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

  5. onmng314
    • 2 years ago
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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)?

  6. onmng314
    • 2 years ago
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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...

  7. MiaKitty
    • 2 years ago
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    I don't know, maybe elimination or substitution?; :)

  8. onmng314
    • 2 years ago
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    I prefer ELIMINATION. Let's do that.

  9. MiaKitty
    • 2 years ago
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    Okay, thx. :)

  10. onmng314
    • 2 years ago
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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 ;)

  11. MiaKitty
    • 2 years ago
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    No, actually, you are supposed to solve it, and then they tell you if you r right. :)

  12. onmng314
    • 2 years ago
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    That is no problem :)

  13. MiaKitty
    • 2 years ago
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    :D

  14. onmng314
    • 2 years ago
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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?

  15. MiaKitty
    • 2 years ago
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    Yes, :)

  16. onmng314
    • 2 years ago
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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.

  17. onmng314
    • 2 years ago
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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?

  18. MiaKitty
    • 2 years ago
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    Yes. :)

  19. onmng314
    • 2 years ago
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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)?

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

  21. onmng314
    • 2 years ago
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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

  22. onmng314
    • 2 years ago
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    Now that we did the appropriate Elimination, can you figure out what X is?

  23. MiaKitty
    • 2 years ago
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    2?

  24. onmng314
    • 2 years ago
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    CORRECT!

  25. onmng314
    • 2 years ago
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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...

  26. MiaKitty
    • 2 years ago
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    Ok, thx so much! :D

  27. onmng314
    • 2 years ago
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    We aren't done :)

  28. MiaKitty
    • 2 years ago
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    I know, let's see, hold on a sec...

  29. MiaKitty
    • 2 years ago
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    Is it -3?

  30. onmng314
    • 2 years ago
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    YES!

  31. onmng314
    • 2 years ago
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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.

  32. MiaKitty
    • 2 years ago
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    Ok, is that it?

  33. onmng314
    • 2 years ago
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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!

  34. MiaKitty
    • 2 years ago
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    Ok, thx! LOL! I will check it out!

  35. onmng314
    • 2 years ago
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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.

  36. MiaKitty
    • 2 years ago
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    Ok. :)

  37. onmng314
    • 2 years ago
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    Do it and report back here with the results. MK.

  38. MiaKitty
    • 2 years ago
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    Hey, they say it is right! :D

  39. onmng314
    • 2 years ago
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    So I was probably right last time, too, huh? LOL

  40. MiaKitty
    • 2 years ago
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    LOL, :) Oh well, :)

  41. MiaKitty
    • 2 years ago
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    You got a medal this time, 2 from me. :)

  42. onmng314
    • 2 years ago
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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 :)

  43. MiaKitty
    • 2 years ago
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    thx, lol! :D

  44. MiaKitty
    • 2 years ago
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    are you in calculus?

  45. onmng314
    • 2 years ago
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    Yes.

  46. onmng314
    • 2 years ago
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    It is the bomb :)

  47. MiaKitty
    • 2 years ago
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    So, you like it, I'm dreading it!

  48. onmng314
    • 2 years ago
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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.

  49. MiaKitty
    • 2 years ago
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    Really, that is so cool! :D I hope I do good in it, lol!

  50. onmng314
    • 2 years ago
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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.

  51. MiaKitty
    • 2 years ago
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    oh, wow, whattopics do you learn, lol?

  52. onmng314
    • 2 years ago
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    Well, I am signing off now. If you ever get stuck, shoot me an email. Byeeeeeeeeee

  53. MiaKitty
    • 2 years ago
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    Ok, byeee!

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