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Math Help - Solve the system by substitution

  1. #1
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    Solve the system by substitution

    1. 3x + 2y = 11
    y = 4x + 8


    3x + 2(-4x + 8) = 11
    3x 8x + 16 = 11
    3x - 8x + (16 - 16) = 11 - 16
    ===> -5x = -5
    ===> x = 1


    y = -4(1) + 8
    y = -4 + 8
    y = 4

    so the solution is (1,4) is that right?





    Am not sure on equation #2

    2. x 3y = 10
    2x 4y = 10
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Patience View Post
    1. 3x + 2y = 11
    y = 4x + 8


    3x + 2(-4x + 8) = 11
    3x 8x + 16 = 11
    3x - 8x + (16 - 16) = 11 - 16
    ===> -5x = -5
    ===> x = 1


    y = -4(1) + 8
    y = -4 + 8
    y = 4

    so the solution is (1,4) is that right?
    This is correct.

    You can simply substitute your answer into both equations to verify your solution:
    1. 3(1) + 2(4) = 11
    3 + 8 = 11
    11 = 11 (check!)

    2. (4)= 4(1) + 8
    4 = -4 + 8
    4 = 4 (check!)

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Patience View Post
    2. x 3y = 10
    2x 4y = 10
    In the interest of using a few fractions as possible solve the top equation for x:
    x = 3y + 10

    and insert this into the bottom equation:
    -2(3y + 10) - 4y = 10

    -6y - 20 - 4y = 10

    -10y - 20 = 10

    -10y = 30

    y = -3

    Thus
    x = 3(-3) + 10 = -9 + 10 = 1

    So your solution is
    (x, y) = (1, -3)

    -Dan
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