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Math Help - Simultaneous equation

  1. #1
    Senior Member Mukilab's Avatar
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    Simultaneous equation

    By eliminating y, find the solutions to the simultaneous equations.

    x^2+y^2=25
    y=x-7

    I've tried many different approaches, come up with 4+ different answers so I have no idea what to do.
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by Mukilab View Post
    By eliminating y, find the solutions to the simultaneous equations.

    x^2+y^2=25
    y=x-7

    I've tried many different approaches, come up with 4+ different answers so I have no idea what to do.
    Substitute the second equation into the first:

    x^2 + (x - 7)^2 = 25.

    Expand, simplify, re-arrange to get a quadratic = 0 and solve for x in the usual way.

    If you need more help, please show all your work and say where you get stuck.
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  3. #3
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Mukilab View Post
    By eliminating y, find the solutions to the simultaneous equations.

    x^2+y^2=25
    y=x-7

    I've tried many different approaches, come up with 4+ different answers so I have no idea what to do.
    You should get two pairs of solutions. It tells you to eliminate y so put x-7 in for y in the first equation

    x^2+(x-7)^2 = 25 When it's expanded and put into standard form we get ......

    Solve using your favourite method although this one factorises to .....

    From this find your value of x and for each one put the value into either equation to find y.
    Last edited by mr fantastic; June 4th 2010 at 06:53 AM. Reason: Sorry, but it's good to leave things for the OP to do.
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  4. #4
    Senior Member Mukilab's Avatar
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    Got 2x^2-14x+24=0 after expanding and simplifying.

    divided by 2

    x^2-7x+12=0

    put into the quadratic equation got
    <br />
x=\frac{7+\sqrt{1}}{2} or x=\frac{7-\sqrt{1}}{2}

    correct?
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  5. #5
    Senior Member Mukilab's Avatar
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    Sorry how is this calculas.
    Actually. What is calculas? All I know that it has some meagre connection to engineering and Newton, I think he created it?

    Time for research.
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  6. #6
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Mukilab View Post
    Got 2x^2-14x+24=0 after expanding and simplifying.

    divided by 2

    x^2-7x+12=0

    put into the quadratic equation got
    <br />
x=\frac{7+\sqrt{1}}{2} or x=\frac{7-\sqrt{1}}{2}

    correct?
    That is correct but since \sqrt{1} = 1 you can simplify your answers

    This is pre-calc rather than calculus and although I don't know how the US system works I'd imagine pre-calc sets you up for calculus. By and large calculus is largely about differentiation (rate of change) and integration (area under a graph). Of course it's far more complicated than that.
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  7. #7
    Senior Member Mukilab's Avatar
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    Thanks, got x=3,4

    Didn't know about the squareroute of 1 being 1, thanks. I guess I just didn't bother to think about that. How silly of me.
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  8. #8
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Mukilab View Post
    Thanks, got x=3,4

    Didn't know about the squareroute of 1 being 1, thanks. I guess I just didn't bother to think about that. How silly of me.
    I got those answers too. Now you can use those values to find y using either equation (equation 2 is simplest). You should get two pairs of values
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