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Math Help - cramers

  1. #1
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    cramers

    use cramers rule to solve for x' and y' in terms of x and y
    x = 3/5x'-4/5y'
    y=4/5x'+3/5y'

    i used cramers rule and deduce that x'=7/5 and y'=-1/5
    but how do i write my answers in terms of x and y?
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    use cramers rule to solve for x' and y' in terms of x and y
    x = 3/5x'-4/5y'
    y=4/5x'+3/5y'

    i used cramers rule and deduce that x'=7/5 and y'=-1/5
    but how do i write my answers in terms of x and y?
    1. For convenience transform the system of equations to:

    \left|\begin{array}{rcl}5x&=&3x'-4y' \\ 5y&=&4x'+3y' \end{array}\right.

    2. Then D=\left|\begin{array}{cc}3&-4\\4&3\end{array} \right| = 25
    and
    D_{x'}=\left|\begin{array}{cc}5x&-4\\5y&3\end{array} \right| = 15x+20y

    3. Thus x'=\frac{D_{x'}}{D} = \frac{15x+20y}{25} = \frac35x+\frac45y

    4. Determine y'.
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