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Math Help - Confusing System of Equations

  1. #1
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    Confusing System of Equations

    This is probably the hardest system of equations problem I have ever encountered.

    "Consider the following system of equations x + y:
    Ax+By=C
    Dx+Ey=F

    Where the constants A,B,C,D,E and F form an arithmetic sequence. How might you characterize the solutions to the system of equations?"
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  2. #2
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    Quote Originally Posted by bleacher39 View Post
    This is probably the hardest system of equations problem I have ever encountered.

    "Consider the following system of equations x + y:
    Ax+By=C
    Dx+Ey=F

    Where the constants A,B,C,D,E and F form an arithmetic sequence. How might you characterize the solutions to the system of equations?"
    If " A,B,C,D,E and F form an arithmetic sequence" then they have some "common difference" d. That is, B= A+ d, C= A+ 2d, D= A+ 3d, E= A+ 4d, and F= A+ 5d.

    That's a cute problem! The answer is surprising.
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  3. #3
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    Hllo, bleacher39!

    Consider the following system of equations: . \begin{array}{c}Ax+By\:=\:C \\ Dx+Ey\:=\:F\end{array}

    . . where the constants A,B,C,D,E,F form an arithmetic sequence.

    How might you characterize the solutions to the system of equations?

    Let the six coefficients be: . a, \;a+d, \;a+2d, \;a+3d, \;a+4d, \;a+5d


    The system becomes: . \begin{array}{ccc}\quad ax \quad+\quad (a+d)y &=& a+2d \\ (a+3d)x + (a+4d)y &=& a+5d \end{array}


    Solve the system (use your favorite method): . x = -1,\;y = 2


    The solution is constant!

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