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Math Help - Simultaneous Equation

  1. #1
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    Simultaneous Equation

    y = 2x - 6
    x^2 - xy + 2y^2 = 16
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  2. #2
    o_O
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    You are given y in terms of x, so directly substitute:

    x^{2} - x\bold{y} + 2\bold{y}^{2} = 16
    x^{2} - x\left(\bold{2x-6}\right) + 2\left(\bold{2x-6}\right)^{2} = 16

    Continue and solve for x.
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  3. #3
    a.a
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    y = 2x - 6
    x^2 - xy + 2y^2 = 16

    => x^2 - x (2x-6) + 2(2x-6)^2 = 16
    x^2 - 2 x^2 + 6x + 2( 4x^2 -12x + 36) = 16
    -x^2 + 6x + 8x^2 -24x + 72 -16 = 0
    7x^2 - 18x + 56=0

    use the quadraic eqn. to solve for x, then when u get the two x values, plug it into y = 2x - 6 and u the two y values
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  4. #4
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    Quote Originally Posted by a.a View Post
    y = 2x - 6
    x^2 - xy + 2y^2 = 16

    => x^2 - x (2x-6) + 2(2x-6)^2 = 16
    x^2 - 2 x^2 + 6x + 2( 4x^2 -12x + 36) = 16
    -x^2 + 6x + 8x^2 -24x + 72 -16 = 0
    7x^2 - 18x + 56=0

    use the quadraic eqn. to solve for x, then when u get the two x values, plug it into y = 2x - 6 and u the two y values
    Should be: x^{2} - 2x^{2} + 6x + 2(4x^{2} - \bold{24x} + 36) = 16
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