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Math Help - Simultaneous Equations.

  1. #1
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    Simultaneous Equations.

    I was wondering if you could doublecheck this question please:

    g) y=2x and  y = 2x^2
    y = 4 and x = 2

    How would I do this?

    h) y= 6 - x^2 and y = 4x +1
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  2. #2
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    Re: Simultaneous Equations.

    Quote Originally Posted by JibblyJabbly View Post
    I was wondering if you could doublecheck this question please:

    g) y=2x and  y = 2x^2
    y = 4 and x = 2

    no

    How would I do this?

    h) y= 6 - x^2 and y = 4x +1

    g)

    2x = 2x^2

    2x - 2x^2 = 0

    2x(1 - x) = 0

    x = 0 and x = 1


    h)

    6-x^2 = 4x+1

    0 = x^2 + 4x - 5

    factor and use the zero product property to solve for x
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  3. #3
    Member sbhatnagar's Avatar
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    Thumbs up Re: Simultaneous Equations.

    In case a graph helps...

    g) y=2x,y=2x^2. The red line is y=2x^2 and the blue line is y=2x.



    Clearly solutions are x=0,1

    h) y=6-x^2,y=4x+1. The red line is y=4x+1 and the blue line is y=6-x^2.



    Clearly solutions are x=1,-5

    The value of y can be calculated just by substituting the value of x or by the graph.
    Last edited by sbhatnagar; October 13th 2011 at 04:32 AM. Reason: change of graph
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  4. #4
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    Re: Simultaneous Equations.

    Yet another way to do (g): y=2x and y=2x^2:

    If x and y are not 0, \frac{y}{y}= /frac{2x^2}{2x}, [tex]1= x[/itex]. And if x= 1, what is y?

    That was "if x and y are not 0". It is easy to check that y is 0 if and only if x is and x= y= 0 satifies both equations.
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