Terri01
Answered

solve each system of equation by multiplying first.


1.) 2x+y=3

-x+3y=-12


2.) 6x+5y=19

2x+3y=5


3)2x+5y=16

-4x+3y=20

Verified Answer :

SmarticalParticals
  1. 2x + y = 3
         -x + 3y = -12  => multiply by 2

         2x + y = 3
        2(-x) + 2(3y) = 2(-12)

         2x + y = 3
        -2x + 6y = -24    Now add the equations
    ________________
               7y = -21
                 y = -3    Substitute back into equation

    2x + y = 3
    2x + (-3) = 3
    2x = 6
    x = 6/2 = 3

    (3, -3)


    2.  6x + 5y = 19
         2x + 3y = 5    => multiply by -3 so the x's will cancel

         6x + 5y = 19
    (-3)2x + (-3)3y = -3(5)

         6x + 5y = 19
        -6x - 9y = -15      now add the 2 equations
    ______________
              -4y = 4
                 y = -1         now substitute back into the equation

    2x + 3y = 5
    2x + 3*-1 = 5
    2x - 3 = 5
    2x = 8
    x = 8/2 = 4

    (4,-1)

    3.  2x + 5y = 16  => multiply by 2 so x's cancel
        -4x + 3y = 20

    (2)2x + (2)5y = (2)16

     4x + 10y = 32
    -4x + 3y  = 20      add the equations
    _____________
             13y = 52
               y = 52/13 = 4  substitute into unchanged equation

    -4x + 3(4) = 20
    -4x + 12 = 20
    -4x = 8
    x = 8/-4 = -2

    (-2, 4)

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