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Math Help - Solution needed to equation - think it is termed a linear equation???

  1. #1
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    Manchetser
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    Solution needed to equation - think it is termed a linear equation???

    Hi

    Excuses first, it is over 20 years since school and I have had no cause to do equations since. I realise this may be rudimentary, no less what is the solution please to:

    4000=(80 * Y) + (160 * x)

    An explanation would ne nice too.

    Many thanks in advance.

    Darren.
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  2. #2
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    Re: Solution needed to equation - think it is termed a linear equation???

    Quote Originally Posted by iksotof View Post
    I realise this may be rudimentary, no less what is the solution please to:
    4000=(80 * Y) + (160 * x)
    There is really no single solution in the sense that I think you mean solution.
    There is a set of solutions, a set of ordered pairs: \left\{\left(x,-2x+50.\right)\right\}.
    Pick any value for x and then you have a value for y=-2x+50
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  3. #3
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    Re: Solution needed to equation - think it is termed a linear equation???

    Thanks for this, I was just after the value of x an y?
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    Re: Solution needed to equation - think it is termed a linear equation???

    Quote Originally Posted by iksotof View Post
    Hi

    Excuses first, it is over 20 years since school and I have had no cause to do equations since. I realise this may be rudimentary, no less what is the solution please to:

    4000=(80 * Y) + (160 * x)

    An explanation would ne nice too.

    Many thanks in advance.

    Darren.
    You can use this Maple code to find nonegative integer solutions :

    Code:
    for x from 0 to 50 do
    for y from 0 to 50 do
    if 50=2*x+y then
    print(x,y);
    end if;
    end do;
    end do;
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  5. #5
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    Re: Solution needed to equation - think it is termed a linear equation???

    Quote Originally Posted by iksotof View Post
    4000=(80 * Y) + (160 * x)
    Divide by 80: 50 = y + 2x

    An integer solution exists for ALL values of x:
    Code:
     x   2x   y   2x+y
     1    2  48    50
     2    4  46    50
     3    6  44    50
    ...
    24   48   2    50
    25   50   0    50
    26   52  -2    50
    27   54  -4    50
    ...
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