Verified Answer :

12x+5y=13 is y=13/5-12/5x
-24y-5y=-11 is y=-11/-5+(24/-5)x

-2x+4y=32 is y=32/4+2/4x
-5x-10y=-20 is y= -20/-10+(5/-10)x

12x+12y=36 is y=36/12-12/12x
-8x-8y=-8 is y=-8/-8+(8/-8)x
  1. 12x + 5y = 13
    -24x - 5y = -11

    First Add these equations to cancel out the y value so we can find the x value.
    (12x + 5y = 13) + (-24x - 5y = -11) 
    = -12x + 0y = 2
    Now we are left with the equation -12x = 2
    Next divide both sides by -12 and x = -1/6
    Now plug x into any of the original two equations to find the y-value.

    12(-1/6) + 5y = 13
    -2 + 5y = 13
    5y = 15
    y = 3

    or 
    -24(-1/6) - 5y = -11
    4 - 5y = -11
    -5y = -15 
    y = 3

    Sp, x = -1/6 and y = 3

    2.-2x + 4y = 32
       -5x - 10y = -20

    First, lets simplify both of the equations.

    (-2x + 4y = 32) / -2 = x - 2y = -16
    (-5x - 10y = -20) / -5 = x + 2y = 4

    Now we have the two equations:

    x - 2y = -16
    x + 2y = 4

    Subtract the equations from each other to cancel out the 'x'.
    (x - 2y = -16) - (x + 2y = 4)
     = -4y = -20 

    -4y = -20 
    Divide by -4
    y = 5

    Now plug 5 in for y in the equations:

    x - 2y = -16
    x + 2y = 4

    x - 10 = -16
    x = -6

    x + 10 = 4
    x = -6

    So , y = 5, and x = -6

    3. 12x + 12y = 36
    -8x - 8y = -8

    Lets also simplify the equations.

    (12x + 12y = 36) / 12 =   x + y = 3
    (-8x - 8y = -8) / -8 = x - y = 1

    Right off the bat you can say that x = 2 and y = 1.

    2 + 1 =3
    2 - 1 = 1

    But mathematically:

    Subtract both equations

    (x + y = 3) - (x - y = 1) 
    = 2y  =  2

    2y = 2
    y = 1

    x + 1 = 3
    x = 2

    x - 1 = 1
    x = 2

    So x = 2 and y = 1;

Related Questions