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Math Help - Pair of simultaneous equations.

  1. #1
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    Pair of simultaneous equations.

    Solve the following pair of simultaneous equations for x and y.
    ax+y=c
    x+by=d
    I don't know why I can't get this one, because it seems pretty simple.
    So far I've done this:
    I multiplied 1 and 2 and got abx+by=cb
    Then I added that and 2 together and got abx+x+2by=cd+d
    x(ab+1)+2by=cd+d
    (cb+d)/(ab+1)=x+2by
    (cd+d)/(ab+1)-2by=x
    However the answer in the back of the book is: x=(d-bc)/(1-ab).
    I'm just not too sure where I went wrong.
    Thanks.
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  2. #2
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    Quote Originally Posted by mandarep View Post
    Solve the following pair of simultaneous equations for x and y.
    ax+y=c
    x+by=d
    I don't know why I can't get this one, because it seems pretty simple.
    So far I've done this:
    I multiplied 1 and 2 and got abx+by=cb
    Then I added that and 2 together and got abx+x+2by=cd+d
    x(ab+1)+2by=cd+d
    (cb+d)/(ab+1)=x+2by
    (cd+d)/(ab+1)-2by=x
    However the answer in the back of the book is: x=(d-bc)/(1-ab).
    I'm just not too sure where I went wrong.
    Thanks.
    You could proceed

    y=c-ax

    and substitute to eliminate y and solve for x

    x+b(c-ax)=d

    x+bc-abx=d

    Now factor out "x" and divide
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  3. #3
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    You have solved the equations for x in terms of y, not in terms of just a,b ,c ,d.

    Start here:
    ax+y=c
    x+by=d

    Multiply the second equation by a:
    ax+y=c
    ax+aby=ad

    Now subtract the second equation from the first:
    (ax+y) - (ax + aby) = c - ad

    Take it from here.

    -Dan
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  4. #4
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    Thanks so much guys.
    I ended up getting y=(ad-c)/(ab-1).
    Now when I sub that into one of the other equations, can I do it into any of them?
    Cause I tried with subbing it in to the first equation.
    I got stuck again with my algebra this time.
    So its ax+(ad-c)/(ab-1)=c.
    What should I do first? The a or something else.
    Thanks again though guys. Your great helpers.
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  5. #5
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    Quote Originally Posted by mandarep View Post
    Thanks so much guys.
    I ended up getting y=(ad-c)/(ab-1).
    Now when I sub that into one of the other equations, can I do it into any of them?
    Cause I tried with subbing it in to the first equation.
    I got stuck again with my algebra this time.
    So its ax+(ad-c)/(ab-1)=c.
    What should I do first? The a or something else.
    Thanks again though guys. Your great helpers.
    You could find the equation for x seperately.

    However, substituting your y, to get x as given...

    \displaystyle\ ax=c-\frac{ad-c}{ab-1}=c+\frac{ad-c}{1-ab}=\frac{c(1-ab)+(ad-c)}{1-ab}

    which comes out as given.
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  6. #6
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    Ok, cool. Thanks so much. =D
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