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Math Help - Solving systems of equation

  1. #1
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    Solving systems of equation

    I really don't know how to solve this system of equation, it's nothing I've ever done before.... mostly they would have identical and the same amount of variables in every column but this one doesn't....

    x + 10 + y + 36 = 210
    80 + 10 + z + y = 180
    36 + z + y + t = 220
    Last edited by asilvester635; November 20th 2012 at 01:11 AM.
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    Re: Solving systems of equation

    Collect like terms, then it will be in a somewhat more familiar format.
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    Re: Solving systems of equation

    10x + 36y = 210
    80z + 10y = 180
    36z + yt = 220

    LIKE THAT???
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    Re: Solving systems of equation

    No, not like that. You have switched some additions to multiplications. Let's take the first one: x + 10 + y + 36 = 210 where we can subtract the 10 and the 36 from both sides to give x + y = 164. Follow that process with the other two and see where it takes you.
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    Re: Solving systems of equation

    x + y = 164
    z + y = 90
    z + y + t = 184

    like that??? if it is, then now what?
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    Re: Solving systems of equation

    No, we cannot change addition to multiplication like that.

    We have:

    x+10+y+36=210

    80+10+z+y=180

    36+z+y+t=220

    Now, if we subtract all the constants on the left side of each equation from the right side, the system becomes

    x+y=164

    z+y=90

    z+y+t=184
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    Re: Solving systems of equation

    Look at equations 2 and 3. Is it not obvious what t is now?
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    Re: Solving systems of equation

    ohhhhhhhh...
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    Re: Solving systems of equation

    okay so t is equal to 94....

    so can i take out the variable t out from the second and third equation and solve the second and third equation like a regular systems of equation?
    Last edited by asilvester635; November 20th 2012 at 02:00 AM.
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    Re: Solving systems of equation

    Well t only appears in the 3rd equation. Using the 1st and 2nd equations I cannot see how you can solve for x, y and z. It seems like you are missing some information.
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    Re: Solving systems of equation

    You will have to solve for two of the remaining variable in terms of the third.
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    Re: Solving systems of equation

    actually there's 3 variables remaining.... this is so hard
    Last edited by asilvester635; November 20th 2012 at 02:21 AM.
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    Re: Solving systems of equation

    Yes, I mention 3 remaining variables. You will have to express 2 of them in terms of the third.

    We know t=94. So this leaves:

    y=164-x

    z=90-y=90-(164-x)=x-74

    This is one way to express the solution, can you find another?
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    Re: Solving systems of equation

    Well this was my original question

    Probability and Statistics homework problem question
    Example 1: Computers, fine arts, economics - this one requires using system of equations

    There are 500 seniors.
    210 are enrolled in computers
    80 do not need any of the 3
    80 are taking only fine arts.

    180 are taking fine arts.
    36 taking only economics and computers
    10 taking only fine arts and computers
    220 taking economics

    Find:
    1.) P(only taking economics)
    2.) P(economics and fine arts)
    3.) P(taking all 3 classes)

    Then this guy gave me this answer
    (View the picture to understand how i got the system) So, you have



    the system
    1) x + 10 + y + 36 = 210
    2) 80 + 10 + z + y = 180
    3) 36 + z + y + t = 220
    4) x + 10 + y + 36 + t + z + 80 = 420

    4 Systems, 4 variables, solve

    Solving systems of equation-pic.png
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  15. #15
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    Re: Solving systems of equation

    Okay, the diagram is correct, but leaves out the 80 not taking any of the 3. The system I get is:

    x+y+z+t=294

    x+y=164

    y+z=90

    y+z+t=184

    Now you have 4 equations and 4 unknowns.
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