Math

Hi! Can someone help me with this? Thanks!

Directions: Solve this equation by doing it twice; one time using the substitution method and one time using the graphing method.

x – 2y = 0
3x – y^2 = 0

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  1. Substitution method:

    x – 2 y = 0 Add 2 y to both sides

    x – 2 y + 2 y = 0 + 2 y

    x = 2 y

    3 x – y ^ 2 = 0

    3 * 2 y - y ^ 2 = 0

    6 y - y ^ 2 = 0

    - y ^ 2 + 6 y = 0 Multiply both sides by - 1

    y ^ 2 - 6 y = 0

    y * y - 6 y = 0

    y * ( y - 6 ) = 0

    Obviously solution y = 0

    and

    y - 6 = 0 Add 6 to both sides

    y - 6 + 6 = 0 + 6

    y = 6

    Now put this solutions in eguation :

    x = 2 y

    For y = 0

    x = 2 y

    x = 2 * 0 = 0

    For y = 6

    x = 2 y

    x = 2 * 6 = 12

    The solutions are :

    x = 0 , y = 0

    and

    x = 12 , y = 6

    You can write this like :

    ( 0 , 0 ) and ( 12 , 6 )

    For graph :

    In google type :

    functions graphs online

    When you see list of results click on :

    rechneronline.de/function-graphs/

    When page be open in blue rectangle type :

    x / 2

    In first gray rectangle type :

    ( 3 x ) ^ ( 1 / 2 )

    In second gray rectangle type :

    - ( 3 x ) ^ ( 1 / 2 )

    Set :

    Range x-axis from - 4 to 16

    Range y-axis from - 4 to 16

    and click option:

    Draw

    You will see graphical solution.

    ________________________________

    Remark :

    If x = 2 y

    then y = x / 2

    and

    3 x – y ^ 2 = 0

    is same :

    y ^ 2 = 3 x

    y = + OR - sqrt ( 3 x )

    y = + OR - ( 3 x ) ^ ( 1 / 2 )

    y = ( 3 x ) ^ ( 1 / 2 )

    and

    y = - ( 3 x ) ^ ( 1 / 2 )

    ____________________________________

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