algebra

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I have to solve this equation using substitution.

3x+5y=10
2x+ 1/2y=24

This is all one problem

  • algebra -

    2 x + ( 1 / 2 ) y = 24 Multiply both sides by 10

    20 x + ( 1 / 2 ) y * 10 = 24 * 10

    20 x + 5 y = 240


    ________________________________________

    3 x + 5 y = 10

    -

    20 x + 5 y = 240
    ________________________________________

    3 x - 20 x + 5 y - 5 y = 10 - 240

    - 17 x = - 230 Divide both sides by - 17

    - 17 x / - 17 = - 230 / - 17

    x = 230 / 17


    2 x + 1 / 2 y = 24

    2 * 230 / 17 + ( 1 / 2 ) y = 24

    460 / 17 + ( 1 / 2 ) y = 24 Subtract 460 / 17 to both sides

    460 / 17 + ( 1 / 2 ) y - 460 / 17 = 24 - 460 / 17

    ( 1 / 2 ) y = 24 - 460 / 17

    ( 1 / 2 ) y = 24 * 17 / 17 - 460 / 17

    ( 1 / 2 ) y = 408 / 17 - 460 / 17

    ( 1 / 2 ) y = - 52 / 17 Multiply both sides by 2

    y = - 104 / 17


    Solutions :

    x = 230 / 17 , y = - 104 / 17

  • algebra -

    using substitution:
    multiply the 2nd by 2
    4x + y = 48
    y = 48-4x

    sub into the 1st
    3x + 5(48-4x) = 10
    3x + 240 - 20x = 10
    -17x = -230
    x = 230/17
    then y = 48-4(230/7) = -104/17

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