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NikkiBxox

  • one year ago

How do you solve a system of equations? I don't have a specific equation that needs to be solved I just need help figuring it out. I cant seem to get it. Medal... Fan...Everything... Thanks.

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  1. freckles
    • one year ago
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    Like x+6=3 ?

  2. freckles
    • one year ago
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    oh system?

  3. freckles
    • one year ago
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    2 variables?

  4. NikkiBxox
    • one year ago
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    Like 2x – 3y = –2 4x + y = 24

  5. freckles
    • one year ago
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    well there are a couple of ways to go about it: elimination, substitution, ..

  6. freckles
    • one year ago
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    Like you can solve the second equation for y. Use that y in the first equation then solve for x.

  7. freckles
    • one year ago
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    So first can you isolate y in the following equation: 4x+y=24

  8. NikkiBxox
    • one year ago
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    y=4x+24?

  9. freckles
    • one year ago
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    Remember whatever you do to one side you must do to the other... You subtracted 4x on the left hand side but added 4x on the right hand side.. It should have been you subtracted 4x on both sides.

  10. freckles
    • one year ago
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    4x+y=24 subtract 4x on both sides 4x+y-4x=24-4x the whole point of this is to get y on the left hand side by itself 4x-4x=0 so you have y=24-4x also can be written as y=-4x+24

  11. NikkiBxox
    • one year ago
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    Makes sense.

  12. freckles
    • one year ago
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    2x – 3y = –2 now we are going to take that y we just found in terms of x and insert in the first equation 2x-3(-4x+24)=-2 Solve this for x.

  13. NikkiBxox
    • one year ago
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    One question would i distribute the -3 to the parenthesis? Or just to PEMDAS

  14. freckles
    • one year ago
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    you have to distribute the distributive property says a(b+c)=ab+ac then you can apply order of operations with common terms on the left hand side

  15. NikkiBxox
    • one year ago
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    Got it. 2x-12-72=-2 -10x-72=-2 -10=70 x=-7

  16. NikkiBxox
    • one year ago
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    Wait. It would be +12

  17. freckles
    • one year ago
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    so you mean to say 2x+12x-72=-2 ?

  18. NikkiBxox
    • one year ago
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    Yes.

  19. freckles
    • one year ago
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    ok and this equation 2x+12x-72=-2 is right so far

  20. NikkiBxox
    • one year ago
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    If I refigure that it would be 2x+12x-72=-2 +72 +72 2x+12x=70 14x=70 x=5

  21. freckles
    • one year ago
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    groovy

  22. freckles
    • one year ago
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    now remember that one equation that we solved for y in terms of x...?

  23. freckles
    • one year ago
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    y=-4x+24 this one!

  24. NikkiBxox
    • one year ago
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    Yeah. Plug it in?

  25. freckles
    • one year ago
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    you can finally find y now by inputting the x you just found into this equation (you could also used the other equation; it just seems easier to plug into this one because we already have y isolated)

  26. freckles
    • one year ago
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    and yes so you have y=-4(5)+24

  27. NikkiBxox
    • one year ago
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    y=4

  28. freckles
    • one year ago
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    This method we used was called substitution. Let me show you elimination on this problem.

  29. freckles
    • one year ago
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    |dw:1444618292337:dw| This was the system .

  30. freckles
    • one year ago
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    To do elimination, we need to choose something to multiply one of the equations (or even both) by so we can get either the x terms to be opposites or the y terms to be opposites What opposite means is like, the opposite of 4x is -4x or the opposite of -3y is 3y. Notice the sign is the only thing that is different when we use the word opposite.

  31. freckles
    • one year ago
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    now we could go about this in two very simple ways

  32. freckles
    • one year ago
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    we could multiply the first equation by -2 or we could multiply the second equation by 3 but do not do both

  33. freckles
    • one year ago
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    |dw:1444618467505:dw| notice if we choose to multiply both sides of the second equation by 3 we have the above

  34. NikkiBxox
    • one year ago
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    That makes a lot of sense!!

  35. freckles
    • one year ago
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    notice we have -3y is the opposite of 3y when you add opposites you get 0 that is why we wanted opposites

  36. freckles
    • one year ago
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    so we are going to add the equations together 2x-3y=-2 12x+3y=72 ----------- 14x+0y=70 14x+0=70 14x=70 do you see we eliminated the y?

  37. freckles
    • one year ago
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    you solved this exact same equation above and got x=5

  38. NikkiBxox
    • one year ago
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    Yes. They are opisites.....OH okay!!

  39. freckles
    • one year ago
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    now using either equation you can find y

  40. freckles
    • one year ago
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    |dw:1444618634766:dw| I like this equation because there is only 1 being multiplied to the y

  41. freckles
    • one year ago
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    so input 5 for x: 4(5)+y=24 20+y=24 y=4

  42. freckles
    • one year ago
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    you could have used the first equation though and got y is 4 2x-3y=-2 2(5)-3y=-2 10-3y=-2 -3y=-12 y=4

  43. freckles
    • one year ago
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    see!?

  44. NikkiBxox
    • one year ago
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    Yes!! Thank you so much!!

  45. freckles
    • one year ago
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    np

  46. freckles
    • one year ago
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    you can also graph the equations and find the intersection i don't really like this method because the solutions aren't always integer pairs like this solution we got for this one

  47. NikkiBxox
    • one year ago
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    Okay. I kinda get how to do that one. These seem easier by far.

  48. freckles
    • one year ago
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    you can solve this one if you want to test yourself: a+2b=5 5a-b=6

  49. NikkiBxox
    • one year ago
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    I definintaly will in the morning. Its time for sleep. Thanks again!

  50. freckles
    • one year ago
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    np if you put your work here whenever you get a chance and tag me and also message me (just to make sure I see it do both), I will check your work

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