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Math Help - basic equations

  1. #1
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    basic equations

    solve for x,y, and z
    31x+12y-24z=105
    18x+24y+z=77
    12x+6y+4z=5
    ive tried doing this several ways, but i get different answers every time. all i am able to really do is get rid of y by multiplying the 3rd equation by 4. after that im just kind of stuck.
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by brandilee View Post
    solve for x,y, and z
    31x+12y-24z=105
    18x+24y+z=77
    12x+6y+4z=5
    ive tried doing this several ways, but i get different answers every time. all i am able to really do is get rid of y by multiplying the 3rd equation by 4. after that im just kind of stuck.
    18x + 24y + z = 77

    z = 77 - 18x - 24y

    12x + 6y + 4(77 - 18x - 24y) = 5

    12x + 6y + 308 - 72x - 96y = 5

    -60x - 90y = -303

    y = \frac{303 - 60x}{90}

    31x + 12y - 24z = 105

    31x + 12( \frac{303 - 60x}{90} ) - 24z = 105

    2790x + 303 - 60x - 2160z = 9450

    2730x+303-2160( 77-18x-24( \frac{303 - 60x}{90} )) = 9147

    2730x - 166320 + 38880x + 174528 - 34560x = 9147

     7050x = 939

     x = 0,1331914894


    You should be able to continue from here, but check my calculations though.
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  3. #3
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    sorry, i wrote that wrong
    the last equation is 12x-6y+4z=5
    im still having trouble following what you did
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  4. #4
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    Try using Cramer's rule, in my opinion its quicker and easier than double elimination or substitution.
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  5. #5
    Bar0n janvdl's Avatar
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    Quote Originally Posted by brandilee View Post
    sorry, i wrote that wrong...
    You have got to be kidding me

    Quote Originally Posted by SnipedYou View Post
    Try using Cramer's rule, in my opinion its quicker and easier than double elimination or substitution.

    Do what he says... I only know the substitution and elimination method as of yet.

    ---------------------

    EDIT: Cramer's Rule
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  6. #6
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    i checked out cramers rule, and have no idea how to use it. thats a little beyond what ive learned so far. this is so frustrating. my class is all online, so theres no real help from teachers
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  7. #7
    Bar0n janvdl's Avatar
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    Quote Originally Posted by brandilee View Post
    i checked out cramers rule, and have no idea how to use it. thats a little beyond what ive learned so far. this is so frustrating. my class is all online, so theres no real help from teachers
    Do you know how to do equations that only have 2 variables? Like only x and y, and no z?
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  8. #8
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    yeah usually
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  9. #9
    Bar0n janvdl's Avatar
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    Quote Originally Posted by brandilee View Post
    yeah usually
    Let's say you have the following(Only for explanatory purposes):

    x + y + z = 3 --- (1)

    2x + 2y + z = 6 --- (2)

    x + y + 2z = 9 --- (3)

    Take equation (1)

    Isolate z:
    z = 3 - x - y --- (4)

    Now take (4) and plug it into (2)

    2x + 2y + (3 - x - y) = 6

    x + 2y + 3 - x - y = 6

    x + y = 3

    y = 3 - x --- (5)


    Now take your new equation and plug that into (3)

    x + y + 2z = 9 --- (3)

    BUT you know that [ y = 3 - x --- (5) ] AND [ z = 3 - x - y --- (4) ]

    Take [ z = 3 - x - y --- (4) ] again:

    z = 3 - x - (3 - x)

    z = 3 - 3 - x + x = 0

    x + (3 - x) + 0 = 9

    3 = 9

    Okay, notice this doesnt work out, it's because I used made up equations and numbers, but this will be the proecedure you'll have to follow.
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