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Math Help - Simultaneous Equations

  1. #1
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    Simultaneous Equations

    Hey guys, I have these two questions, which I am confused about. If anyone could help me I would be very grateful!

    "Solve the following simultaenous equations using an analytical method (either elimination or by substitution of methods) and then check your answers by plotting their graphs on the same set of axes.
    <br />
y = 2 + 2x

    3y = 20 - x

    ________________________

    second question

    Find the roots of the following Quadratic equations using the methods specified:

    x^2 - 6x + 9 = 0 by Factorisation

    3x^2 - 8x + 2 = 0 using the quadratic solution formula.
    Last edited by mr fantastic; January 25th 2009 at 02:24 PM. Reason: Deleted a hotell
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  2. #2
    Member TheMasterMind's Avatar
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    Quote Originally Posted by Mathtard View Post
    Hey guys, I have these two questions, which I am confused about. If anyone could help me I would be very grateful!

    "Solve the following simultaenous equations using an analytical method (either elimination or by substitution of methods) and then check your answers by plotting their graphs on the same set of axes.
    <br />
y = 2 + 2x

    3y = 20 - x

    ________________________

    second question

    Find the roots of the following Quadratic equations using the methods specified:

    x^2 - 6x + 9 = 0 by Factorisation

    3x^2 - 8x + 2 = 0 using the quadratic solution formula.
    1.

    y=2+2x

    3y=20-x

    use substitution it is easiest method here

    3(2+2x)=20-x

    6+6x=20-x

    7x=14

    x=14div7

    x=2

    sub back into original to get y

    y=2+2(2

    y=2+4

    y=6

    therefore they intersect at (2,6)

    check it yourself

    2.

    I) (x-3)(x-3)

    II) use x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

    where a=3,b=-8 and c=2
    Last edited by mr fantastic; January 25th 2009 at 02:24 PM. Reason: Edited quote
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  3. #3
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    Thank you very much for your help, I understand this alot better now. Thank you!!!
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