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algebra

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Explain why the addition method might be preformed over the substitution method for solving the system
2x – 3y = 10
5x + 2y = 6
What is the solution of this system?

  • algebra -

    2 x – 3 y = 10 Multiply both sides by 2

    4 x - 6 y = 20



    5 x + 2 y = 6 Multiply both sides by 3

    15 x + 6 y = 18




    4 x - 6 y = 20

    +

    15 x + 6 y = 18

    ----------------

    4 x + 15 x - 6 y + 6 y = 20 + 18


    19 x = 38 Divide both sides by 19

    x = 38 / 19

    x = 2


    To get the value of y you need to use the substitution method.

    Substitute x = 2

    into equation

    2 x - 3 y = 10

    2 * 2 - 3 y = 10

    4 - 3 y = 10

    - 3 y = 10 - 4

    - 3 y = 6 Divide both sides by - 3

    y = 6 / - 3

    y = - 2

  • algebra -

    The point of intersection of the graphs of the equations of the system

    Ax – 4y = 9
    4x + By = –1

    is (–1, –3). Explain how to find the values of A and B, then find these values.

  • algebra -

    (-1 , -3) = ( x,y)

    put the X and Y values into the first equation,

    Ax-4y=9

    A(-1)- 4(-3)= 9

    -A + 12=9

    -A=-3

    A= 3 [ Multiply by (-1)]

    Now put the X and Y values to the second equation,

    4( -1) +B( -3) =-1

    -4- 3B=-1

    -3B= 3

    B=-1 [ Multiply by negative (-1)]

    Just check are those ans is right, put the all values to the equation......

    3(-1)-4(-3)=9

    9=9

    And, 4(-1)+(-1)(-3)=-1

    -4 + 3=-1

    -1 = -1

    So, (A,B)= ( 3, -1 )

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