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Math Help - i dont understand subtituting linear into quadratic

  1. #1
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    i dont understand subtituting linear into quadratic

    how would you substiture these two equations to find the values of x and y for these two questions.

    1)y=x-5 2)3x-4y=25
    y=2x^2-3x-3 and x^2+y^2=25





    im not understanding substitution...could you please help me with these two questions showing the steps.
    thank you
    kishan
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  2. #2
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    Solve the linear equation for y (expressed as a function of x) and insert the result into the quadratic equation. The result is an equation you should be able to solve for x.

    For example, in the second problem the equation you solve for x is x^2+((3x-25)/4))^2=25.
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  3. #3
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    plz

    can u show it to me in steps because im confused
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  4. #4
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    Quote Originally Posted by kishan View Post
    can u show it to me in steps because im confused
    OK, here's the first one:

    The two equations can be combined to x-5=2x^2-3x-3. This is easy to simplify to x^2-2x+1=0, or if you prefer, (x-1)^2=0. The only solution is x=1. Use the first equation to find y:

    y=x-5=1-5=-4

    So the answer is x=1, y=-4.

    The second problem:

    Solve 3x-4y=25 for y. The result is y=(3x-25)/4. Insert this into the second equation:
    25=x^2+y^2=x^2+(\frac{3x-25}{4})^2
    =x^2+\frac{1}{16}(9x^2+625-150x)
    =\frac{25}{16}x^2-\frac{150}{16}x+\frac{625}{16}

    Multiply both sides with 16/25.

    16=x^2-6x+25
    x^2-6x+9=0
    (x-3)^2=0
    x=3
    y=(3*3-25)/4=-4

    So the answer is x=3, y=-4.
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