Math

Solve each system by using the elimination method. Make sure to write your answer in (x,y) form.

1.) 3x-5y=2

2x+5y=13

2.) 3x+11y=4
-2x-5y=9

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  1. 1.)

    3 x - 5 y = 2 Add 5y to both sides

    3 x - 5 y + 5 y = 2 + 5 y

    3 x = 2 + 5 y Subtract 2 to both sides

    3 x - 2 = 2 + 5 y - 2

    3 x - 2 = 5 y

    5 y = 3 x - 2

    2 x + 5 y = 13

    2 x + 3 x - 2 = 13

    5 x - 2 = 13 Add 2 to both sides

    5 x - 2 + 2 = 13 + 2

    5 x = 15 Divide both sides by 5

    5 x / 5 = 15 / 5

    x = 3

    3 x - 5 y = 2

    3 * 3 - 5 y = 2

    9 - 5 y = 2 Add 5 y to both sides

    9 + 2 - 5 y + 5 y = 2 + 5 y

    9 = 2 + 5 y Subtract 2 to both sides

    9 - 2 = 2 + 5 y - 2

    7 = 5 y

    5 y = 7 Divide both sides by 5

    5 y / 5 = 7 / 5

    y = 7 / 5

    x = 3 , y = 7 / 5

    In ( x , y ) form :

    ( 3 , 7 / 5 )

    2.)

    3 x + 11 y = 4 Subtract 3 x to both sides

    3 x + 11 y - 3 x = 4 - 3 x

    11 y = 4 - 3 x Divide both sides by 11

    11 y / 11 = ( 4 - 3 x ) / 11

    y = ( 4 - 3 x ) / 11

    - 2 x - 5 y = 9 Multiply both sides by -1

    - 2 x * ( - 1 ) - 5 y * ( - 1 ) = 9 * ( - 1 )

    2 x + 5 y = - 9

    2 x + 5 * ( 4 - 3 x ) / 11 = - 9

    2 x * 11 / 11 + 5 * ( 4 - 3 x ) / 11 = - 9

    22 x / 11 + ( 20 - 15 x ) / 11 = - 9

    22 x / 11 + 20 / 11 - 15 x / 11 = - 9

    7 x / 11 + 20 / 11 = - 9 Multiply both sides by 11

    7 x * 11 / 11 + 20 * 11 / 11 = - 9 * 11

    7 x + 20 = - 99 Subtract 20 to both sides

    7 x + 20 - 20 = - 99 - 20

    7 x + 20 - 20 = - 99 - 20

    7 x = - 119 Divide both sides by 7

    7 x / 7 = - 119 / 7

    x = - 17

    3 x + 11 y = 4

    3 * ( - 17 ) + 11 y = 4

    - 51 + 11 y = 4 Add 51 to both sides

    - 51 + 11 y + 51 = 4 + 51

    11 y = 55 Divide both sides by 11

    11 y / 11 = 55 / 11

    y = 5

    x = - 17 , y = 5

    In ( x , y ) form :

    ( - 17 , 5 )

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